The 30-year-old spent the second half of last season on loan at Rovers and scored seven goals in 18 appearances.
The former Swansea and Watford forward signed on a free transfer following his released by Sunderland.
“He’s constantly been on the phone ringing me asking what is happening,” he told BBC Radio Lancashire.
“It’s nice to have that as a player and someone wanting you that much.
“A lot of the lads have been texting me asking if I’m coming back and I must admit I am delighted to be here.
“I had a tough time at Sunderland, nothing really worked out there so confidence was probably at a low. To come here and do so well and have the lads get behind me and everything else, it was a massive sway in the right direction.
“For a loan player to come in, you’ve got to work for the team and I think I showed that. I think the fans took to that and I’m glad they’re happy that I’m back.”
Graham is the third new arrival at Ewood Park since Owen Coyle took over this summer, and the second forward after Anthony Stokes.
Asked if their will be more strikers incoming, Coyle added: “If the question is ‘are we finished yet in that department’ then I would say no, we’ve still got our eyes open and looking about.
“We’re still looking to add a very creative midfield player.
“There is one that I’ve got my eye on that can find that final pass, he is pleasing on the eye and is only going to get better – but that one’s a bit more complicated. He is at an elite club and it would be a year-long loan.”