The 26-year-old, who has helped Bedford reach the Championship play-offs this season, will complete his move to Allianz Park in the summer.
"We have been watching Mark for some time," Sarries director of rugby Mark McCall said.
"He has proved himself to be one of the most impressive lock forwards in the Championship."
Flanagan has represented Ireland at Under-20 level and has previously had spells at Leinster and French side Stade Montois.
Premiership leaders Saracens have agreed to sign Bedford Blues lock Mark Flanagan on a two-year deal.