The 28-year-old, who has made 219 Bath appearances, will make the move when his existing Bath contract expires at the end of the season.
Borthwick's departure will come as a hammer-blow to Bath, who are currently second in the Guinness Premiership and through to this season's European Challenge Cup quarter-finals.
Borthwick has been a Bath player for the past 10 years, and his form this season has been key to a string of impressive Premiership and European results.
He said: "After 10 years here (at Bath), I feel the time is right for a new challenge. A change in club provides that, and I am excited about what the future holds.
"I am very confident that the excellent player group at Bath will get stronger, and my commitment for the rest of the season will continue to be of the highest standard."
Bath head coach Steve Meehan, who recently agreed a new two-year deal at the Recreation Ground, added: "We need to concentrate on the remainder of the season.
"Steve Borthwick has committed himself to still playing hard for the club until the end of the season.
"Over the coming months, positive announcements will be made that will reassure fans we will continue to move in the right direction."
Borthwick made his Premiership debut for Bath against Saracens in 1998, while the west country club's next league fixture is at Vicarage Road on Sunday week.
He will leave a huge gap in the Bath squad, both in terms of his leadership skills and playing ability, having carved a reputation as arguably English rugby's finest technical lineout exponent.
Saracens rugby director Alan Gaffney said: "Steve is an excellent lineout forward who is in the prime of his career, and we are delighted that he is joining the club.
"It is a huge plus for Saracens. His ability in the set-piece and all around the pitch means he will fit in well with the expansive and attacking style of rugby we are developing at the club and want to play in the years to come.
"He will be a great asset as part of our ongoing aim to be among the elite sides of Europe."