The Fulham player, who has not been on the losing side since joining Posh in September, has agreed a three-and-a-half year contract at London Road.
He will officially put pen to paper when the transfer window reopens in January.
"Gaby has agreed terms and it's a big signing for the club," manager Darren Ferguson told the Peterborough Evening Telegraph.
"There are one or two things to iron out, but he should sign a three-and-a-half year deal soon.
"He is a top-class defender who will be able to cope comfortably with football in the Championship which is the aim of us all."