The Scotland Under-21 international, 20 has scored 17 goals in 93 appearances for Livi.
Snodgrass' arrival came a day after Anthony Elding sealed his exit from Elland Road by completing a move to League One rivals Crewe Alexandra
He is excited about the chance to try his luck at Elland Road.
"This move is a dream come true. There were a few other clubs from the south that were interested, but this is a club of big stature," he said.
"Over the years a lot of Scots have done well here and I want to try and get to the next level now."