The 26-year-old moved to Ipswich on a short-term deal in September, but he failed to make a competitive appearance for the Championship outfit.
In fact, the Wales international midfielder has not featured in a competitive game since May 2014 because of a knee injury.
Collison is delighted to have found a new club and is looking forward to the 2015-16 campaign.
Thanks for all the messages... Can't wait to get started now.. I have missed it so much— Jack collison (@Jcollison31) May 29, 2015
Peterborough finished ninth in the League One table in the 2014-15 season with 63 points from 46 matches, six points behind sixth-placed Chesterfield.