The Welsh outfit confirmed on Wednesday that a deal to sign the midfielder had been completed.
It has been widely reported that Swansea paid £16.5m for the Leicester City graduate, who has penned a four-year contract at the Liberty Stadium.
After finalising his move, Clucas told the club's official website: "There were a couple of clubs interested, but I felt Swansea was the perfect fit for me. I've seen a lot of Swansea and one of the main reasons I decided to come here was because of the way they play football. I think it suits me.
"I had a bitter sweet season last year with relegation. Because of my playing background, I never thought I would play in the Premier League so I relished every game I played. From the first time I kicked a ball in the Premier League it was a dream come true.
"Once you've had a taste for the Premier League you always want to go back. So when the chance came up for me to do that again at Swansea, I grabbed the opportunity with both hands."
Clucas could make his debut against Crystal Palace this weekend.