The dominating South African central defender, who recently received a first call-up for his national side, passed a medical on Friday and took the weekend to make a decision over his future.
Posh manager Barry Fry offered Arber a three-year contract and the club captaincy but the player believes Oldham are better equipped to mount a promotion push next season.
Oldham chief Brian Talbot previously tried to take Arber to Rushden & Diamonds and will be delighted with his latest capture.
Meanwhile, goalkeeper Steve Corry has been handed a three-month contract - commencing on July 1.
Corry joined Oldham last season on a short-term deal and will now be aiming to impress sufficiently to earn a longer contract.
Jamaican international Jermaine Johnson has received confirmation that he has been granted a work permit for next season.
The talented wide man signed for The Latics in the close-season from Premiership outfit Bolton Wanderers.
