The League One new-boys swooped for the out-of-contract 25-year-old, who was first choice for Posh last season, making 37 appearances.
Jones began his career at Leyton Orient and left to join Exeter, where he made 158 appearances, before moving to Peterborough in January last year.
He said: "I have followed the club's success over the last two years and it didn't take me long to decide I wanted to be part of an ambitious club like Crawley.
"It's a great set-up with Steve Coppell and Sean O'Driscoll involved and I can't wait to get started in pre-season in July."
Crawley chief executive Alan Williams added: "Paul is an outstanding acquisition for the club. He is a commanding presence and has lots of experience at Championship level.
"We are delighted he is here and we think our supporters will enjoy watching him and we look forward to him enjoying a long and successful career with the club."