The 34-year-old arrives as a free agent having left West Bromwich Albion by mutual consent in January.
The Scotland international started his career in his home country with Livingston before moving to Leeds United in 2008.
He enjoyed a prolific spell at Elland Road in League One and was a key figure in their promotion to the Championship in 2010, before he earned a move to Premier League side Norwich City in 2012.
After a two-year spell at Carrow Road, Snodgrass earned promotion with Hull City before later spells in the Premier League with West Ham, Aston Villa and most recently West Brom, where he started five times this season, the last of which in the 1-1 draw against Middlesbrough in November.
The midfielder was also a regular for Scotland national team between 2011 and 2019, earning 28 caps and scoring seven times in that period.
Manager Nathan Jones said: “We’ve brought Snoddy in because of the experience he gives us, the wonderful quality that he has, and it became the right time to do it.
“We’ve been looking for a left footed midfield player for a while and we’ve picked up a few injuries in the midfield area, and so he ticks a lot of boxes.
“He’s got play-off experience, he’s got Premier League experience and he is known to a number of our players and staff, so we know he’s the type of character that we want in here.
“It gives us something different now we are in the final third of the season and he’ll give us a little bit of a push towards the run-in.
“We know the quality he’s got, we know where he’s been, and with the number of injuries we’ve had, it gives us cover in that area because our midfielders have had to do big shifts.
“We’ve had Luke Berry and Jordan Clark out for a spell, and then Allan and Pelly have had to do massive shifts along with Henri, so the time was right, and I thank the board for doing it.”