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."
Fletcher revealed manager Martin O'Neill 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."