The 27-year-old England international is currently serving a two-year ban having admitted taking cocaine during his time with Bath.
That admission ensured Stevens missed out on a chance to tour with the Lions to his native South Africa last summer, four years after he made his Lions debut against Bay of Plenty on the 2005 tour of New Zealand.
Stevens had courted interest from London Wasps, with Bath also keen to resign him, but he has now officially agreed to join Sarries on January 19, 2011.
"This is a massively significant signing for the club - it demonstrates the scale of our ambition, and it also shows that top players recognise Saracens as a well run club with a bright future," said Saracens' director of rugby Brendan Venter.
"Matt is a world-class prop with his best rugby ahead of him, and I'm sure he will flourish in our environment."
Despite his decision being made public almost a year before his ban comes to an end, Stevens will not be able to train with Sarries or be integrated into the club in any way shape or form until his ban expires.
""I am looking forward to launching the next phase of my rugby career at Saracens in January next year," said Stevens.
"I have many great memories and friends in Bath, but there is something special happening at Saracens and I am very eager to be part of it."