The 25-year-old joined Sunderland on a four-year contract last week, with Wolves mustering £12m a transfer fee.
"It took its time," said Fletcher. "Three or four bids were rejected and I was sitting there thinking it was never going to happen.
"I think I've had it too easy in the past. Up until now, it's just kind of happened and it's me who has been called and told 'You've been sold'.
"For it to drag on for so long was a little bit frustrating, but I am happy to be here now."
However, Fletcher has fond memories of his two years at Wolves.
"I was [sad to leave]. I enjoyed every minute I was at Wolves," he said.
"The boys were fantastic, and the staff and the fans, so it was a bit disappointing. But I have moved on now and I am looking forward to playing here."
Fletcher started his career at Scottish club Hibernian in 2004 and joined Burnley in 2009.