The 22-year-old will be expected to make his Posh debut at London Road on Saturday when they face fellow strugglers Barnsley.
McGovern has been without a club since having his contract terminated by mutual consent with the Carrow Road club.
He recently had a successful trial with Scottish Premier League side Livingston but with the club unable to sign players before January's transfer window opens, he decided to try his luck elsewhere.
McGovern comes in for the departing Marc Joseph, who is expected to complete his move to Division Three side Hull City by the end of this week.
Peterborough boss Barry Fry told the club's official website that he was delighted to sign the defender.
Fry said: "Brian adapted very well for us in the friendly against Arsenal and with Marc leaving us, we were a bit short of cover in the defence.
"He is 22-years-old and I am sure with the support from the fans, he will settle in quickly at London Road."
McGovern was pleased to have an opportunity to play with The Posh and is looking forward to helping them climb out of trouble in the league.
McGovern said: "I was all set to sign for Livingston, but I was told I wouldn't be able to start playing for them until January, so I came down to England as I know quite a few managers in the Nationwide League.
"Barry gave me a call and told me he required a defender because Marc has joined Hull and I was happy to sign.
"It was my first training session this morning and already I know what a good team spirit this club has and that is important if you are struggling in the league.
"I am looking forward to the game against Barnsley and it is important we get a good result."
Fry has further added to his ranks by signing Luton Town goalkeeper Mark Ovendale on loan as cover for the injured Mark Tyler.
Tyler has been ruled out for up to 14 weeks following successful surgery on a fractured bone in his hand.
With The Posh's usual number one out for around three and a half months and Dan Connor the only senior custodian at his disposal, Fry will look to use Ovendale in Tyler's place for the short-term.
Fry added: "Mark always plays well against us and he will do a good job for the club.
"With Mark Tyler out for a long while, we needed another goalkeeper at the club as Dan Connor is the only registered senior shot-stopper at London Road.
"He will hopefully train with us on Friday and go straight into the side for the game against Barnsley.
"I hope the supporters encourage him and he won't let anyone down."
Ovendale joined The Hatters from Bournemouth for £425,000 in 2000 but has made few appearances since being at Kenilworth Road.
