The 29-year-old helped the Bears win the One-Day Cup last season, scoring 257 runs at an average of 64.25 in 10 appearances in the competition.
Evans joined Warwickshire in 2010 and also won the County Championship in 2012 and the T20 Blast in 2014.
Sussex head coach Mark Davis described Evans as "player of great ability".
He added: "He plays in all formats of the game and is a brilliant acquisition for the club. I believe Laurie's best years are in front of him, and he is driven to achieve his undoubted potential."
Evans has predominantly played white-ball cricket for Warwickshire, but has scored 2,926 runs at an average of 34.02 in first-class cricket.
He had a spell on loan with Northamptonshire in 2016.
Bears first-team coach Jim Troughton said: "Laurie has played an important part in our white-ball cricket for several years, but has been unable to secure a regular place in the team for first-class cricket.
"Whilst it's naturally disappointing that Laurie has decided that he no longer wants to play for Warwickshire, we do not wish to stand in the way of his ambitions in the game and we wish him the very best in his career with Sussex.
"We are also aware that he has been keen to move closer to his family in London and being based on the south coast will work better for him."

17 July 2016 Last updated at 19:25 BST
Arriving into Belfast International Airport on Sunday morning, most of them told BBC News NI reporter Claire Graham they were happy to be home.
Sussex have signed batsman Laurie Evans on a three-year contract after Warwickshire released him a year early from his deal at Edgbaston.
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Northern Ireland holidaymakers returning from Turkey have been giving their reaction to the attempted military coup on Friday.