The 27-year-old agreed a two-year deal to become Sky Blues boss Steven Pressley's first signing of the summer and, after turning down a new contract at the Posh, he did not hesitate once City came calling.
He told the club's website: "I'm delighted to get a deal done because Coventry City is a big club.
"The talks I had with the manager had a massive influence on my decision. He's been fantastic and it's pretty clear that he knows what he wants to do with the club and the direction he wants to take it.
"I can't wait to get going. The manager places a huge importance on fitness because of the intensity that he likes to play and train at and the way he likes his team to press the game and that's great news for me because that's what I like."
Swanson played 49 times for Posh last term, netting on three occasions. The Scot previously played for Dundee United and Berwick.
He added: "I really feel that Coventry City is going places. We just need to get back on track and hopefully this year can be our year.
"The training ground blew me away. I saw it as I was driving in and thought to myself that this is where I want to train.
"I'm excited about playing football again and while the manager is obviously focused on fitness he also wants to get the footballs out as soon as possible so I'm really looking forward to that.
"I want to be playing in the Championship again and hopefully I can do that with Coventry."