Previous head coach Neil Harris left Cambridge last month just before they lost 1-0 at home to Posh in a key League One game. Posh also beat Cambridge by a record 5-0 margin at London Road in November.
Monk began his managerial career with Swansea City and his former clubs also include Middlesbrough and Birmingham. He has been out of football since he was sacked by Wednesday in November 2020 after 14 months at Hillsborough.
Cambridge majority owner Paul Barry said: “He is a coach of high pedigree, has managed at the top level and impressed us all with his leadership skills, clarity of thinking and his analysis of Cambridge United – both the squad and the club.
“Although he has had opportunities to get back into the game over recent times, he has been waiting for the right one. Like us, he sees this as a project and we are pleased he has decided to join us on the journey ahead.”
Cambridge are in danger of relegation. They sit just two places and four points above the relegation zone after lost their last four matches.
Monk’s first game in charge will be against Northampton Town at the Abbey Stadium on Saturday. Northampton visit Posh for a League One game on Tuesday.
