Graham sealed a move to Sunderland on Deadline Day, but that was only after he snubbed interest from Boro and also Norwich.
Boro were hopeful of beating rivals Sunderland to Graham, who started his career at the Riverside Stadium.
Swansea agreed to Boro's offer of money plus Marvin Emnes, but Graham did not want to drop out of the top-flight.
"Boro was an option, but no more than that," said Graham.
"Of course, Middlesbrough was my first club and so there was still a pull there, but I really wanted to carry on playing in the Premier League.
"The chance to return home to the North East was a massive attraction for me.
"I have been away for a long time, living and playing in Watford and in Swansea.
"So to come home and play for a big football club up here is great and once Sunderland came in for me and I had the chance to play in the Premier League at a club of this size, it was always going to be this club that I wanted to move to."