In February 2012, Snodgrass was appointed captain of Leeds, but he rejected a new contract offer and moved to Norwich City later that year.

Born in Glasgow, Snodgrass grew up in the city's Gallowgate area;[5] he played boys' club football for a team affiliated with Rangers alongside future international teammate James McArthur who is a month younger and lived a few blocks away.

He felt that he had little chance of breaking through at Parkhead, so chose Livingston, joining their setup at the same time as another East End boy who would go on to play for Scotland, Graham Dorrans.

[8] After recovering from a broken metatarsal, he moved to Stirling Albion on loan for the remainder of the 2006–07 season on 30 January 2007 to step up his recovery from injury.

After joining Leeds, Snodgrass came into the side for the first game of the season to make his debut against Scunthorpe United, gaining an assist after setting up Enoch Showunmi's headed goal.

[citation needed] After initially struggling to hold a regular place in the starting line-up, Snodgrass established himself after a string of impressive performances throughout November and December, which saw the young winger score four goals in seven games during a poor run of form for the Yorkshire club, culminating in the sacking of manager Gary McAllister.

[citation needed] Snodgrass scored a late winner against Milton Keynes Dons in a 1–0 win for Leeds for his first league goal of the season.

[13] On 27 July 2010, Snodgrass was believed to have suffered a serious knee injury during the pre-season game away to Norwegian team Brann after falling victim to a horrendous challenge by David Nielsen.

[19] To help gain match fitness after his injury, Snodgrass played 90 minutes in a closed-doors friendly against Middlesbrough.

[20] Snodgrass returned to Leeds' squad after injury when he was named on the bench the game against Doncaster Rovers, he came on as a second-half substitute replacing Ross McCormack.

[21] Snodgrass came on as a second-half substitute against Sheffield United and managed to assist Leeds' late winner for Bradley Johnson, however his game ended on a sour note when he was sent off for two yellow cards.

[22] Snodgrass returned from suspension for Leeds against Ipswich Town, replacing Luciano Becchio in the starting lineup and scored his first goal of the season.

[40] Snodgrass was appointed club captain by new Leeds manager Neil Warnock, ahead of his first game in charge against Portsmouth on 25 February.

Snodgrass scored his first goal of the 2013–14 season with a "free-kick from around 20 yards that looped over the wall and into the bottom-left corner of the net" in a 3–1 win over West Ham United on 9 November.

[48] He scored again on 23 February 2014 against Tottenham after a cutting through ball from Bradley Johnson, holding off the defender and placing it past goalkeeper Hugo Lloris from just inside the box.

On 30 June 2014, Hull City signed Snodgrass for an undisclosed fee, believed to exceed £6 million, on a three-year contract.

[53] On 9 January 2016, in the third-round of the FA Cup match against Brighton & Hove Albion, he scored a penalty to take the team through the next round.

[59] In August 2017, having played 15 games for West Ham without scoring, Snodgrass was told that he was free to leave the club either permanently or on loan.

[61] In March 2019, Snodgrass was charged by the Football Association with allegedly abusing anti-doping officials who were visiting West Ham's training ground on 6 February 2019 to conduct out-of-competition testing.

[73] On 31 January 2022 it was announced Snodgrass had left the club by mutual consent, having last started a game in a 3–0 home victory against Bristol City in October.

[83] Snodgrass was called up to the senior Scotland squad by George Burley for the first time for their friendly against Japan in October 2009.

[84] Snodgrass made his full international debut on 9 February 2011, coming on as a substitute against Northern Ireland in a 2011 Nations Cup match.

[86] Snodgrass was ruled out of Scotland's Nations Cup matches against Wales and the Republic of Ireland with a back injury.

[88][89] On 7 June 2013, during 2014 FIFA World Cup qualifying, he scored the only goal in a 1–0 win against Croatia, inflicting their first competitive defeat at home since they lost 4–1 to England in 2008.

[82] On 24 January 2011, an arrest warrant was issued for Snodgrass after he failed to turn up to court regarding an alleged driving offence.

[94] A spokesman for Leeds United said that the non-appearance was due to a misunderstanding and that Snodgrass was working with the judicial authorities to resolve the matter.

[94] On 3 March 2017, another arrest warrant was issued for him after he failed to attend his trial for allegedly driving in Glasgow with a baby being held in the arms of a passenger.