Born in Maryport, Cumbria, Murray began his playing career playing for non-League side Workington Reds before joining American team Wilmington Hammerheads in 2004. He spent one season with the North Carolina club playing 14 times and scoring three goals in the USL Professional League. After his time in America he joined Barrow where he scored seven goals in seven games. Murray then signed for Conference National side Carlisle United and was part of the Conference play-off-winning team in 2005 and League Two-winning side a season later.

Rochdale manager Steve Parkin then signed Murray on loan until January 2007. Murray then signed for the club on a contract until 2009, for an undisclosed fee. He made his first start for Rochdale in their 7–1 defeat away at Lincoln City on 21 October 2006. His first goal was a 59th-minute equaliser in their match with Barnet on 18 November, but Rochdale lost the match 3–2. Murray made 31 league appearances in his first season with the club and scored 16 goals.

Murray had been linked with a transfer to League One team Brighton & Hove Albion throughout the January transfer window, and finally completed his move to the Withdean Stadium on 25 January 2008 for a reported £300,000. He made his debut four days later, coming on as a 61st-minute substitute for Nathan Elder during the 1–0 defeat away to Northampton Town. He started Albion’s next match, on 2 February at home to Crewe Alexandra, and scored two goals on his home debut in the 3–0 victory. Murray scored nine goals for Brighton during the 2007–08 season.

Despite suffering several injuries during the 2008–09 season, Murray made 28 appearances and scored 12 goals. In the team’s 4–0 win over Barnet in the first round of the League Cup on 12 August 2008, he was sent off. On 27 September, he netted twice in a 2–2 draw at Northampton Town; his second put the team ahead in added time before Adebayo Akinfenwa equalised. A week later he scored twice in the opening seven minutes and finished with his first hat-trick for the team in a 3–3 draw with Cheltenham Town.

On 17 October 2009, Murray won and converted a penalty for a consolation goal in a 2–1 defeat at Tranmere Rovers, but three minutes later was sent off for a second yellow card. He scored four times in Brighton’s 5–2 win away at Wycombe Wanderers on 28 December, a result which moved Brighton out of the relegation zone. Murray’s season ended on 24 April 2010 with Brighton’s 2–1 win over Bristol Rovers to stay in the division; he was sent off ten minutes after coming on as a substitute for Chris Holroyd.

The 2010–11 season proved to be Murray’s best season thus far at Brighton, scoring 22 goals and finishing runner-up to Craig Mackail-Smith as League One top scorer. This included a hat-trick on 1 January 2011 in a 5–0 win over Leyton Orient. On 20 May, the club confirmed that Murray had rejected their final offer of a new contract, so would be available on a free transfer when his contract expired.

On 24 May 2011, Murray signed a three-year contract with Crystal Palace, Brighton’s main rivals. Manager Dougie Freedman said that Murray was the type of player that his squad needed.

On 22 September 2012, Murray scored a hat-trick including two penalties against Cardiff City, and repeated the feat on 6 November against Ipswich Town in a 5–0 victory despite missing a third penalty. He scored twice in a 3–0 home win over Brighton on 1 December, a result which put Palace on top of the league table.

On 2 February 2013, Murray scored twice in four minutes against South London rivals Charlton Athletic as Palace came from behind to win 2–1. In March, he lost out to Watford’s Matěj Vydra as Championship Player of the Season. On 28 March, Murray signed a new three-year contract with Crystal Palace. Murray missed the play-off final, in which Palace secured promotion to the Premier League, having suffered a serious knee injury in the semi-final against Brighton.

Murray came back from injury as a 72nd-minute substitute for Jason Puncheon on 8 February 2014 in a 3–1 home win against West Bromwhich Albion. On 2 March, he scored his only goal of the season and his first in the Premier League, winning a late penalty against Swansea City after being fouled by Chico Flores and converting it past Michel Vorm to earn a 1–1 away draw.

On 1 September 2014, transfer deadline day, Murray moved to Championship club Reading on loan until 1 January 2015. He scored twice in his debut match in a 3–0 win over Fulham. Murray scored eight goals in 18 league games for Reading, ending on 26 December with a brace in a 2–2 draw at Brighton where he opened the scoring after 39 seconds.

On 7 August 2015, Crystal Palace rejected a £3 million bid for Murray from Premier League rivals Bournemouth. On 1 September, an improved bid of £4 million was accepted, and Murray joined the club on a three-year-deal. He scored his first goal for Bournemouth on 3 October in a 1–1 draw with Watford, a fellow newly promoted team, but had a penalty saved late on. He scored a consolation goal in the following match, a 5–1 loss at Manchester City. In December, he scored a late headed goal to clinch a win against reigning champions Chelsea at Stamford Bridge.

On 3 July 2016, Murray returned to Brighton & Hove Albion on a season-long loan. His second debut for the Sussex side came on 6 August away to Derby County, while his first goal in his second spell came at home to Nottingham Forest six days later; he scored his second in the same match as Albion won 3–0. Brighton repeated that scoreline at Falmer Stadium four days later against Rotherham United, and Murray was again on the scoresheet. On 29 October, Murray scored a hat-trick against Norwich City at Falmer as the Seagulls secured a 5–0 win, and on 18 November he scored his 150th career League goal in a 1–1 draw with Aston Villa.

On 31 January 2017, Murray re-signed permanently for Brighton & Hove Albion on a deal until June 2019. He had scored 15 goals in 28 appearances while on loan to the club in the first half of the season. He contributed 8 more league goals in the remainder of the season, including the opening goal in a 2–1 home win against Wigan Athletic on 17 April that sealed Brighton’s promotion to the Premier League for the first time in their history.

Newly promoted Brighton made a positive start to their inaugural Premier League season, sitting in 8th place after eleven games. An unbeaten run of four games from mid-October coincided with Murray hitting a good run of form, with the striker scoring four goals in the three games preceding the November international break. His scoring run began with two against West Ham United in a 3–0 away win, and he followed it up with goals against Southampton at home and Swansea City away, earning Brighton four points. On 8 January 2018, Murray scored the winning goal in Brighton’s 2–1 victory over arch rivals and former club Crystal Palace to eliminate them from the FA Cup at the third-round stage.

On 1 September 2018 Murray scored twice to take Brighton from 2–0 down to draw 2–2 with Fulham. His 100th goal for Albion, the only goal of the match at home to Wolverhampton Wanderers on 27 October, made him just the second man – after Tommy Cook with 123 – to reach that milestone. Murray signed a one-year contract extension on 13 November that runs to the summer of 2020. After 9 games without scoring, on 29 January 2019 Murray scored another two goals against Fulham in a 4–2 away defeat. This time Fulham came back from 2 goals behind, and won. On 6 February 2019 Murray scored another two goals this time coming off the bench in a fourth round FA Cup replay against West Brom where his goals put Brighton 2–1 and 3–1 up in the 3–1 victory. On 9 March 2019 Murray scored his 100th league goal for The Seagulls at his former club and bitter rivals Crystal Palace in a 2–1 away victory. This win meant Brighton won the double over Palace.

On 24 January 2018, Murray and his wife Stacey were arrested on suspicion of tax fraud totalling £1.1 million. In April 2019, HMRC announced that they had concluded their criminal investigation and no charges had been brought.

In August 2019, Murray appeared on A Question of Sport, where he was teamed up with team captain and former cricketer Phil Tufnell and snooker player Mark Selby. He asked to call up former team mate Bruno during his teams loss in the long running game show.

On 1 September 2020, Murray signed for Championship club Watford on a one-year loan deal. 10 days later he made his debut in Watford’s opening game of the season coming on as a sub in a 1–0 home win over Middlesbrough.