McCann's switch to Posh means he will be playing League One rather than Championship football next season.
Peterborough director of football Barry Fry said: "From day one the manager identified Grant as a key signing and spent several weeks talking to him."
McCann, a former West Ham trainee, has become boss Gary Johnson's second summer signing after striker Dave Hibbert penned a three-year deal.
I have no doubt that if Gary was not the manager, Grant would not be here
Barry Fry
Fry continued: "The manager was keen to get the signing sorted as soon as possible. I have no doubt that if Gary was not the manager, Grant would not be here.
"We have to thank the chairman Darragh MacAnthony because he has backed the manager superbly in the transfer market and I am sure everyone will agree Grant is a fantastic signing."
Meanwhile it is expected that Johnson will continue his recruitment with the signing of right-back Mark Little in the coming days.
Source: BBC Sport
Source: BBC Sport