Pietersen completed his reintegration by appearing against India 'A' earlier this week and Swann is full of praise for the 32-year-old.
The spinner said: "Kevin's reintegration has been a seamless process and it needed to happen. Everyone was wondering how it would go and whether it would be as easy as it has been.
"A lot of credit for that has to be given to Kevin for the way he has come in. It's just business as usual and the dressing room is a very happy place this week.
"And that's what we need to be if we are going to have a chance of beating India over here. We need to be a very united dressing room."
The first Test between England and India begins on November 15 in Ahmedabad.