Burke, 24, is due to return from an Achilles injury for round eight for the Crusaders.
Burke, who is qualified to play for England, has signed a three-year deal with the side which has lost England international five-eighths Owen Farrell.
Since making his Crusaders' debut in 2020, Burke has played 33 times for the side.
A product of the Crusaders' Academy, he also played for Canterbury in 48 games, scoring 409 points in the Bunnings Cup, and was a member of the New Zealand Under-20s in the world championship in Argentina.
Burke said on the Saracens' website that he was excited to be joining Saracens. The club is sitting in third place on the Premiership ladder.
Saracens director of rugby Mark McCall said, "Fergus is a very exciting addition to our squad and the Premiership. His playing ability and potential is obvious and we have been impressed by his ambition and desire to take his game to the next level.
"Fergus joins a group of players who we believe can take the club forward in the years to come."