The Scot admitted he was a fortunate victim of Everton's current financial circumstances.
"If the club had multi millions to spend they would spend it and that's the reality and if they did have the money to spend then possibly I wouldn't have been coming back," he told the Liverpool Echo.
"So that's the state of the club at the minute.
"But I'm delighted I've got the chance to come back and hopefully I can prove my worth to the squad. The other offers were good for different reasons.
"The Wolves offer I didn't have to move house and my kids could stay at the same school.
"The Celtic one I could have moved back to Scotland, but I spoke to the manager here and he told me he wanted me to come back. He showed faith in me to bring me back and this is a great club and a great chance to play Premier League football again.
"I think fans saw glimpses of my best football last time, but it just wasn't on a consistent basis. That was one of my reasons for leaving in the first place. I wanted to go and test myself and play every week and I did that at Birmingham. They got relegated twice, but got promoted, had the highest finish they've had in the league for I don't know how long and won the League Cup, so I've had a good experience being away.
"But I'm glad to be back and I hope it can be different this time in that I can push to be a regular and find a level of consistency."