He made 53 appearances for the Addicks before being let go and made the switch to Barnet in September.
"He had a bad injury at Charlton but has been playing at Barnet," Posh boss Darren Ferguson told the club website.
"He has done well since he joined us on trial, so we have taken him until the end of the season."
Basey featured 14 times for the Bees, scoring once, and was released three days after a 4-2 defeat by Stevenage, in which he scored a spectacular own goal.
Barnet boss Paul Fairclough said at the time: "It soon became apparent to me that Grant's heart was not really fully involved in the task we have on our hands.
"That is not to criticise Grant but given the position we are in I am looking for warriors."
Stevenage 4-2 Barnet: Basey lobs his own goalkeeper
Source: BBC Sport
Source: BBC Sport