The 25-year-old Scotland international made his debut for the club in last night's 2-0 Capital One Cup victory over Morecambe after Wolves finally agreed to sell him to the Black Cats following a summer-long pursuit.
Fletcher admitted he feared at one point that the deal, which cost the Wearsiders around ?12million, would not go through, but his wish was finally granted on Friday.
He said: "It took its time. 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 little a bit frustrating, but I am happy to be here now."
Sunderland boss Martin O'Neill snapped up the Scot just hours before also landing England winger Adam Johnson on a day when he managed to get his hands on his top targets.
Fletcher revealed the Ulsterman did not have to work too hard to persuade him his future lay at the Stadium of Light.
He said: "When you speak to the Gaffer, you walk away and you feel like a million dollars, so to work under him, I'm looking forward to it."
For all Fletcher is delighted to have won a return to the Barclays Premier League, he will look back on his time at Molineux with fondness despite suffering a second relegation in three seasons - he also went down with Burnley in 2009-10 - at the end of the last campaign.
Asked if he was sad to leave, he said: "I was. I enjoyed every minute I was at Wolves.
"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 will attempt to build his reputation at Sunderland, although he remains out of the international picture amid a major difference of opinion with Scotland boss Craig Levein.
But the frontman was diplomatic when asked about what the future might hold for him.
He said: "Hopefully I can get a few games under my belt here and get a few goals and we will see what happens."