The forward, 34, leaves Crystal Palace, after spending the last eight years at Selhurst Park, on a free transfer.
Freedman had two spells with the Eagles, scoring almost 100 League goals for the club.
He has also played for Barnet, Wolves and Nottingham Forest during a varied career, and netted five times in 11 appearances during a loan spell with Leeds United at the end of last season.
The Shrimpers also signed Portsmouth midfielder Jean-Francois Christophe on a one-month loan deal on transfer deadline day.