England's home series against his native South Africa having been dropped for sending "provocative texts" to Proteas players.
But with then England captain Andrew Strauss having since retired, Pietersen has been welcomed back into a top-order that would otherwise be short on experience not to mention talent.
Pietersen, in an England team now captained by Alastair Cook, showed his class with a typically aggressive 110 against Haryana in the tourists' final warm-up match.
And Swann said there was no reason why the team, who lost their world number one ranking to South Africa in England earlier this year, would struggle to be united on the field as they go in search of a first Test series win in India since 1984/85.
"Of course we can be a unit again," Swann told online magazine Wisden EXTRA.
"You don't have to like everyone you play with for the team to do well. But once you turn up, you have to pull together and be professional about things.
"I don't think I've played in many teams in which everyone gets on with everybody else.
"That is just the way of the world. It is like in business: you don't always choose who you work with, you just get along. The bottom line is that the dressing-room is fine."
Swann added: "Pietersen is always going to be a fairly polarising character because of the way he is. But there is no reason why he cannot be part of a very successful England team, and be a very successful part of that team."
Meanwhile, with Indian pitches known for being spin-friendly surfaces, Swann is set to play a key role with the ball having recently returned to India after a brief break from the tour in order to spend time with his family after his daughter, who is only a few weeks old, was taken ill.
And the Nottinghamshire bowler, on the brink of becoming England's most successful Test off-spinner, is relishing his chance to shine.
"My motivation has never changed," said the 33-year-old, a veteran of 46 Tests. "I love playing Test cricket. I love being involved in this team, being the guy that can influence a win.
"My motivation is to be winning games for England. I want to be man-of-the-match, the centre of attention. That's what keeps driving me on.
"If I didn't think we could win in India, I wouldn't be going. The moment I considered that we couldn't win somewhere would be the day I retired."
Since making a stunning Test debut in Chennai in 2008, when he took the wickets of Gautam Gambhir and Rahul Dravid in his first over, Swann has collected 192 Test wickets, leaving him one shy of equalling the record by an England off-spinner set by Jim Laker in the 1950s.
"Yes, when you get near a milestone or someone else's personal record, comparisons are flattering," Swann said.
"But our records are only comparable on a piece of paper, because we played in different eras, and it would be arrogant to claim that you were as good as or better than those who went before you."