Williams, 25, can play full-back or wing and has 38 caps for Wales, as well as 100 Scarlets appearances.
The move could limit his international appearances, under the senior selection policy which only allows three non-Wales based players to be selected.
"Liam is arguably one of the most talented backs in Europe," director of rugby Mark McCall said.
In a statement released by the Scarlets, Williams said: "I will continue to give my all in the Scarlets jersey and will hopefully have an opportunity to play for silverware at the end of this season with a what is a great group of boys."
European and Premiership champions Saracens have already confirmed France hooker Christopher Tolofua will move to Allianz Park next season.
Williams' arrival adds new competition for Alex Goode and Sean Maitland at full-back, an area in which Sarries have had to add cover in fellow Welshman Andrew Fenby this season.
As for Scarlets, Williams' exit would put them in a position to bring Toulon and Wales full-back Leigh Halfpenny to the region.
The Welsh Rugby Union said it had made "the best offer it can" to take him back to Welsh rugby.
Chris Jones, BBC Radio 5 live rugby union reporter
It has been an open secret for some time.
With 38 Wales caps, he has developed into one of the finest attacking running backs in Europe and he is sure to thrive at Saracens, a club which has an outstanding reputation for developing and looking after its players.
But it is a blow for the domestic game in Wales. Scarlets say they fought hard to keep him and my understanding is that he was offered a dual-contract with the Welsh Rugby Union.
He will now have to rely on a wildcard selection next season to play for the Wales national side.
Wales back Liam Williams will join Saracens from Scarlets on a three-year deal from the start of 2017-18.