He also played Gaelic football with the Cork minor team. Delaney was a Munster minor football winner with the team in 1999 and shone for his club, St Michael’s. He struck 2–2 in an All-Ireland semi-final defeat to Mayo that year, before he committed fully to soccer.

He was brought to England by Peter Taylor at Leicester City, where he made eight FA Premier League appearances. He had spells on loan at Stockport County, Huddersfield Town and Mansfield Town. Whilst at Stockport, he scored his first career goal in a match against Rotherham United. Taylor later made Delaney his first signing for Hull City, on 16 October 2002, for a fee of £50,000.

On 18 January 2008 Delaney signed for Queens Park Rangers on a three-and-a-half-year contract. On 8 March 2008 Delaney scored his first goal for QPR in a 2–1 away defeat to Sheffield Wednesday.

On 13 May 2008, Delaney was called up to the Republic of Ireland squad for the first time by the new manager Giovanni Trapattoni. On 4 May 2011, he was called into the Irish squad for the 2011 Nations Cup games against Northern Ireland and Scotland. On 24 May 2011, he started and played the full 90 minutes against Northern Ireland as Ireland beat them 5–0. On 11 October 2013, he made a belated competitive debut in a World Cup qualifier against Germany.

On 2 July 2009, Delaney signed for Ipswich Town on a two-year contract for a fee of £750,000, £250,000 if Ipswich reached the play-offs and an extra £100,000 after he has made 50 appearances for the club. He suffered a freak injury in the following year’s pre-season which almost cost him his life. A blood clot in his thigh resulted in him potentially losing a leg but he was rushed to an emergency surgery procedure that resolved the issue. He scored his first goal for the club in the East Anglian derby in November 2010, before being sent off following a straight red card. He left the club by mutual consent in August 2012.

On 31 August 2012, following his departure from Ipswich, Delaney signed for Crystal Palace on a short-term contract until January 2013. He scored his first goal for the club in Palace’s 4–3 comeback against Burnley on 6 October. Due to Delaney’s impressive start to his Palace career, he signed a new contract on 22 November 2012, which expired summer 2014. He scored his first ever goal in the Premier League in a 3–3 draw against Liverpool, with his initial 25-yard shot deflected slightly into the net by Glen Johnson. Palace were 3–0 down at the time, but Delaney’s goal combined with two goals from Dwight Gayle made it 3–3. Delaney was a regular for Palace for their first four seasons back in the Premier League and stayed at the club until the end of the 2017–18 season, making a total of 193 appearances in all competitions, scoring seven goals.

After the end of the 2017–18 Premier League season, Cork City announced that Delaney had signed with the club, and returned on 1 July 2018 after his contract with Palace expired and the Irish transfer window opened. He made 14 appearances, scoring one goal, before leaving the club at the end of the season.