Snodgrass makes the move to Midlands following a short stint in London with the Hammers, where he failed to nail down a consistent spot in the starting eleven.
He links up with former boss Steve Bruce in the Championship, with whom he won promotion to the Premier League while at Hull City in the 2015/16 season.
Villa the clear choice for Snodgrass
The 29-year-old told avfc.co.uk that he is "delighted to join" the Villans and that in the end "it was an easy decision to come here" despite having "offers from other clubs".
He said that it was "the name Aston Villa with all its history, tradition, fanbase" that attracted him to the club after a frustrating period at West Ham, adding that "seeing [Aston Villa] in the Championship doesn’t look right".
Snodgrass continued by saying that he wants to be "part of that journey back up to the Premier League" and is "raring to go" with four games of the Championship season played.
The Scottish international joined the Hammers in the January transfer window for a fee of £10.2million after scoring seven in 20 for Hull City during the first half of last season.
The move did not go quite as Snodgrass hoped however as he failed to score in any of his 15 appearances for the Hammers while recording just two assists.
Winger has impressed in the Championship previously
He started his career with Scottish First Division side Livingston and graduated to their first-team in 2004, before moving to then League One Leeds United in 2008 for under £300,000.
He went on to score 41 goals in 187 games for the Whites across four seasons, with two of those in League One before the club were promoted to the Championship in 2010.
His performances earned him a move to Norwich City in 2012 and it was at Carrow Road where he would first play in the Premier League, scoring six and recording eight assists in 37 games for the Canaries in his first season.
Following their relegation at the end of the 2013/14 season Snodgrass opted to remain in the top-flight with newly promoted Hull City but in a cruel twist of fate was ruled out for the season with a knee injury, Hull were relegated to the Championship while Norwich returned to the Premier League at the first attempt.
Snodgrass helped the Tigers to promotion via the play-offs in 2015/16 however and returned to the top-flight under Bruce, where his performances led him to a move to West Ham.