Graham became the record signing for Swansea City when he completed his £3.5m move from Watford on completion of his medical yesterday.
And he told the official site "I'm delighted to have got everything sorted
I had been away on holiday (Dubai) so couldn't do it any sooner. Now I just can't wait to get started.
"I know Brendan has been an admirer of me for some time, which is flattering, and he had a bid rejected for me at the start of the season.
"He came to Carlisle to sign me when he was manager at Watford. But by the time I had arrived at Vicarage Road he had taken over at Reading.
"I still had two great years at Watford. It's a great club with great people and fans and I'd like to thank them for everything they've done for me.
"But it's a new chapter for me now at Swansea and I'm looking forward to it and having a good season in the Premier League.
"I've had a good chat with the gaffer (Brendan) and I liked what he hade to say. He's driven; I'm driven and I'm looking forward to working with him and establishing a good relationship with him, the team and the fans.
"It's going to be a difficult task because there are no easy games in the Premier League. But the squad at Swansea is very strong and the way they play is suited to the Premier League. Hopefully I can come in and add to that.
"The way Swansea play is how football should be played and was a massive factor, together with my chat with Brendan, to me coming here.
"No disrespect to Blackpool last season, but I think Swansea has a better squad with better players. But, similar to them, we have to go in there with a 'no fear factor', enjoy the football and stick to the way Swansea played in the Championship. We've got nothing to lose.''