The 22-year-old, whose contract expires this summer, has elected to join the U's permanently after spending time on loan with the League One side this season
Having come through the youth ranks with the north London club, Eastmond was part of the side which won the FA Youth Cup in 2009.
He became a regular for the reserves and made 10 senior appearances for the Gunners, but was unable to cement a first-team place and spent time on loan with Millwall, Wycombe and, this season, Colchester.
The 22-year-old was out of contract this summer, and has elected to sign permanently with the U's.
A statement on the Gunners' website read: "Everyone at Arsenal would like to thank Craig for his contribution to the club, and wish him well for his future career."