He had also been linked with a move to Essendon, but the Saints are believed to have won the race for the 25-year-old.
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Stevens has played 74 games for the Dogs, but struggled to play regular senior football under Luke Beveridge, managing just 24 games over the past two years.
Stevens was first drafted by the Eagles in 2009, playing 11 games in three seasons, before being traded to the Whitten Oval.
He has averaged 17.7 disposals, 3.3 marks, 3.6 tackles and 2.4 inside 50s per game in his career.