Davidson was scouted and subsequently signed by St Johnstone. His performances for the Perth club attracted interest from Premiership clubs, resulting in a move to Blackburn Rovers in February 1998 for £1.75m, a St Johnstone club record. He spent two years at Ewood Park, making 66 League appearances and scoring once, against West Ham United.

Davidson made his first full international appearance for Scotland in September 1998, in a goalless draw with Lithuania. He played regularly during the UEFA Euro 2000 qualifying campaign, including the second leg of the play-off tie with England. After six years out of the national team, he was included in George Burley’s squad to face Northern Ireland in August 2008, but did not play. He then started in a 4–0 defeat against Norway in August 2009. Davidson ended up winning 19 caps in total, with his final appearance being in a 2–0 win against Macedonia in September 2009.

Davidson joined Leicester City in July 2000, for a fee of £2.75m, and he remained with the Foxes for four years, making over 100 appearances. He was signed by Preston North End in 2004 on a free transfer and was later appointed club captain. His time at Deepdale was dominated by recurring injury problems, but he still managed to make over 160 appearances for Preston.

On 26 May 2011, Davidson rejoined his first professional club St Johnstone on a one-year deal on a free transfer after being released from Preston North End earlier in the year. He made his debut on 23 July against Aberdeen. He scored his first goal for St Johnstone in a 3–1 win over Dunfermline on 25 February 2012. St Johnstone chairman Steve Brown had initially indicated the club would not be offering Davidson a new contract due to his age, with Davidson’s form forcing him into a rethink. Davidson extended his contract with St Johnstone for another season in March 2012.

Davidson was appointed assistant manager of St Johnstone in June 2013, while retaining his registration as a player. He did not make any playing appearances in the 2013–14 season, during which St Johnstone won the 2013–14 Scottish Cup. Davidson temporarily took charge of the team in March 2014, while manager Tommy Wright was in hospital having a gall bladder operation. He was added to the coaching staff of the Scotland national football team during 2017.

Davidson left St Johnstone in June 2018, when he became a first-team coach at Stoke City. Davidson linked up with Gary Rowett, who had been his teammate at Leicester. Rowett and Davidson both left Stoke on 8 January 2019.

In February 2019, Davidson became first-team coach at Dunfermline Athletic. He left this position in the summer of 2019, and was then appointed assistant manager of Millwall in October 2019 (again working with Gary Rowett).

He was appointed manager of St Johnstone in June 2020, succeeding Tommy Wright.