Solbakken, a midfielder, started his career in Norway, playing for his local lower league team Grue. After five seasons with Grue he moved to HamKam, a then-second tier club, in 1989.

He was the club’s top goalscorer in the 1990 season, where he netted nine times. The following season he scored 14 goals to help the club to promotion to the top-flight Norwegian Premier League. After narrowly avoiding relegation in his first season at the top level, Solbakken was part of the HamKam side that finished 5th in 1993 – a position they have not bettered since.

In 1994, he transferred to their Premier League rivals Lillestrøm where he finished as runner-up in the league during his first season. Although the club finished in fourth during the following campaign, Solbakken’s performances saw him win the Kniksen award as the Norwegian Midfielder of the Season.

Solbakken made his international debut for the Norway national football team on 9 March 1994, in a 3–1 friendly win in Wales. Although he was not named in the squad for the 1994 World Cup, he became a regular feature in the squad soon after.

He was appointed club captain by Lillestrøm and helped the side again finish runners-up in 1996 before he serving one final season in 1997 for the Canaries. In total, he made 99 league appearances for the club, scoring 34 times.

In October 1997, Solbakken joined English Premier League club Wimbledon for £250,000. In his six league games for Wimbledon, Solbakken scored one goal against West Ham United, and was twice named “man of the match”, but he fell out with team manager Joe Kinnear and was banned from club training shortly thereafter.

He was quickly sold to Danish side Aalborg BK in March 1998. Solbakken became Aalborg BK’s captain, and guided the club to the 1998–99 Danish Superliga championship, as well as the final of the 1998–99 Danish Cup tournament. He won Danish football’s Player of the Year Award in 2000. In total, he played 79 games and scored 13 goals for AaB in the Danish Superliga.

In August 2000, he departed to Danish league rivals Copenhagen. Solbakken quickly became a regular player in the side and helped push them to the top of the table but he was unable to complete the season after suffering a heart attack in March 2001. The club went on to win the 2001 Superliga championship and give Solbakken a second championship medal as a player.

During training on 13 March 2001, Solbakken had a heart attack. He was rapidly attended to by the club doctor, Frank Odgaard, who found that Solbakken’s heart had stopped beating. Odgaard asked a player to call an ambulance and to tell them it was critical, while he continued to administer cardiac massage. Upon the ambulance’s arrival, Solbakken was pronounced clinically dead at the scene. On the way to the hospital in the ambulance, he was revived nearly seven minutes later.

In 2002, Solbakken returned to Norway and started his managerial career at his old club HamKam, positioned at the second tier. He had great success at HamKam, as the club won the league and was promoted to the top-flight Tippeligaen. His “resurrection”, and the “salvation” (i.e. promotion) of HamKam, earned him the nickname “Ståle Salvatore”, often cited in Norwegian press since.

The next season, Solbakken managed HamKam to a fifth place in the Tippeligaen 2004 season, and he won the 2004 Kniksen award as Norwegian Manager of the Year. In late 2005, Solbakken was named as new manager of another of his former clubs, Copenhagen.

In his first years at the club, Solbakken guided Copenhagen to the 2006 and 2007 Danish Superliga championship, as well as the 2006 Royal League trophy. He managed Copenhagen through to the group stage of the 2006–07 UEFA Champions League, after beating Ajax in the final qualifying round on 23 August 2006. Copenhagen finished last in its group, though they won a meriting 1–0 victory against later semi-finalists Manchester United.

In May 2009, Solbakken led Copenhagen to the Double of both the 2009 Danish Cup and the 2009 Superliga championship, the seventh championship in club history. On 3 November 2009, it was announced that he would not renew his contract which ended on 30 June 2011. Instead, he agreed a letter of intent to become Norway national team manager either in January 2012 or after the Euro 2012, should Norway qualify. However, this agreement was ultimately not to come to fruition.

On 15 May 2011, it was announced that Solbakken would take over as manager of 1. FC Köln of the German Bundesliga from sporting director Volker Finke, who acted as interim manager after Frank Schaefer quit during the season. Solbakken had been due to take the Norway national team job in January 2012 but Köln bought out his contract for a reported €400,000.

Solbakken was dismissed by Köln on 12 April 2012 following a 0–4 loss at Mainz, with the team sat in 16th place. He was replaced by former coach Frank Schaefer who oversaw the final four games of the season during which the club dropped to 17th place and so were relegated.

On 11 May 2012, English club Wolverhampton Wanderers announced that Solbakken was to become their new manager. He officially took over from acting manager Terry Connor on 1 July 2012. Solbakken began his Wolves tenure with the club in the Football League Championship having been relegated from the English Premier League at the end of the 2011–12 season. His first competitive game in charge was a League Cup tie against Aldershot Town, which his side won on penalties.

Solbakken failed to stop the club’s slump that had brought relegation and despite at one time lifting the club to third place, they had slumped as low as 18th by the turn of the year. He was sacked on 5 January 2013 following an FA Cup elimination by non-league Luton Town, which was his fourth consecutive defeat.

On 21 August 2013, Solbakken returned as head coach of Copenhagen, two years after his departure.

Solbakken had a seven year reign at Copenhagen in which he won three championships in 2016, 2017 and 2019. Howeveer, due to a bad start to the 2020–21 Danish Superliga and a failure to qualify for the 2020–21 UEFA Europa League, Solbakken was fired as manager on 10 October 2020.