Norwich City have completed the signing of goalkeeper Jake Kean following his release from Blackburn Rovers.
Paul Anderson has become Bradford's seventh signing of the summer, agreeing terms on a two-year deal with the Bantams.
The Wales captain has ended speculation over his future by signing a four-year deal to keep him at the Liberty Stadium until 2018.
The news is a massive boost for Swansea after Williams was linked with a number of their Premier League rivals - with Sunderland seeing one bid for the centre-back knocked back.
Williams admits it was flattering to be mentioned as a target for other clubs, but maintains that he always felt he would end up staying at Swansea.
"I didn't feel I was going to end up anywhere else anyway so I was always focused on Swansea City," Williams told Sky Sports News Radio.
"Obviously I just tried to relax over the summer and recuperate and really watched it play out in the media like everybody else did.
"I didn't really say anything. There was a lot of speculation but I have kind of got used to it, especially over the last couple of years. It seems to be the same every year, just with different teams.
"I didn't pay too much attention [to the speculation] and I have just seen what was going on and waited for the agreement with Swansea as we were both quite comfortable to sign here.”
Asked if he was flattered by the interest, Williams added: "Yeah, definitely, I always say I just take it as a compliment as it means you are doing something right and that's just the way I look at it
"I don't look too much in the speculation and stuff until something happens.
“I am used to it, it is not the first time it's happened. It is what it is."
Williams admitted the influence of manager Garry Monk played a big part in his decision to prolong his stay in South Wales.
"Definitely, I have been in game long enough now to know it is important to have a good relationship with the manager, if you have a relationship or if you enjoying working with them, and I have got both," he added.
"He is a friend of mine. I played with him for six years and I worked under him for a couple months at the end of last season and really enjoyed that time working for him, the way he trains and way he sets up his teams, so it was important.
"It just means I was more than happy to sign again."