The move to France, effective from on July 1, potentially ends Farrell's international career after he decided to take a break from representing his country for mental health reasons.
Farrell, 32, has played 112 matches for England and scored 10 tries. He was part of the side that won three Six Nations titles and reached the World Cup final in 2019.
The former England captain joined Premiership Rugby side Saracens in 2008 as a teenager, and has represented them in 237 matches.
Owen Farrell celebrates after Saracens won the 2016 European Champions Cup final against Racing 92. (AP PHOTO)
Speaking after he announced his Six Nations squad last Wednesday, England head coach Steve Borthwick said: "I think what's important is that Owen makes a decision that is right for Owen and his family.
"Will a player of Owen's calibre be missed if he chooses to play outside of England? Yes, of course.
"Do I want him in some point in the future to come back? Yes. But I also want him to do what's right for him and his family and have the experiences and the memories that he wants to make."
Farrell's decision will be a major blow for Saracens, although Racing's announcement will not have caught them on the hop as rugby director Mark McCall recently revealed that he knew what decision Farrell had made.
"Everybody realises the adventure we've been on is coming to an end, and there is a new adventure about to start with a group of younger players we are incredibly excited about who have signed up for the longer term," McCall said last week.
"I suppose all good things come to an end, and there is a re-energising effect and impact of a new group.
"There is a new dawn coming, and it is exciting for everybody."
Farrell's Saracens teammate Jamie George will skipper England in the upcoming Six Nations Championship, which kicks off on February 2.
Six-time French Top 14 champions Racing 92 are top of the table in their ongoing league campaign, with 40 points after 12 matches. They lead second-placed Begles-Bordeaux by four points.
With PA.
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