The experienced midfielder signed a two-year contract with Blues after making over 280 appearances during six years at with the Clarets.
"You weigh up every offer on its merit," said Elliott in the Lancashire Telegraph.
"I had a great time at Burnley. I knew everybody there and knew what I was doing every day. I was very comfortable there.
"It would have been easy for me to stay and keep going along and see it out. But I don't think that would have been the best thing for any party. It wouldn't have been the best thing for me to get the best out of myself professionally.
"I've had one or two chances to move in the past and it wasn't quite right. It just feels like a good time and a good club for me to be going on to.
"It's a little bit weird but I think it's sunk in now I've trained and been at the club and met the lads.
"I've been going to Burnley day in, day out for the last six years. That, allied to the good times I've had there, it became a big part of my life.
"It's a big change to not be going there anymore. It's exciting too."