Moyes has been speaking publicly for the first time since being named as Sir Alex Ferguson's successor at Old Trafford, and paid fulsome tribute to the Everton chairman Bill Kenwright and the supporters.
"The fans have been great to me from day one here. I would like to say thank you for that support they've always given me," he said.
"It was very difficult meeting with the chairman this week. I have great respect for him and we've had a great relationship
"The chairman has never been critical of me and he has always tried to give me everything he possibly can to support me.
"I wasn't planning on leaving. My contract was running out but we were planning for pre-season. All we've ever done here is keep planning."
When asked if he had considered turning down United's approach, Moyes said: "I have to be honest and say no."
Moyes, who ends his 11-year stint on Merseyside with a home game against West Ham before bringing the curtain down at Stamford Bridge next week, admits it will be a wrench to leave.
"I think Sunday will be emotional because I've been so close to the players and the people around Goodison," he added.
"As a manager I might have got more mellow. I hope I've not lost that intensity but maybe learned to use it in the right ways."
The former Preston boss also admitted that he would be happy to give the Everton board his advice on his successor before taking up the United job on July 1.
"I'm sure there will be lots of good people interested in this job and no wonder, because it is a great place to work," he continued.
"Walter Smith recommended me, and if there's anything I can do, I'll be more than happy to help.
"Whoever comes in as manager will get a well-run club, a great set of players. I'm disappointed to be leaving such a great club.
"This club when I took over was bobbing along near the bottom of the league. Now we're competing around fifth or sixth spot every season.
"When I came in and mentioned the People's Club it was from my heart, it was how I felt about the club. The 11 years haven't disappointed me.
"The players this year have been exceptional and I would hate to think Sunday and next week are about David Moyes."
Manchester United captain Nemanja Vidic has backed "winner" Moyes to build on Ferguson's legacy at Old Trafford.
Vidic said: "I'm looking forward to working with David and I believe I will have the same success I had with Sir Alex.
"David and Sir Alex share some similarities - they are very passionate, they are both winners and you can see the way they approach the games and how they run things.
"David Moyes did a great job with Everton. He is a man who gets his players to work hard and show discipline.
"He did that well with Everton because in the last few years they've been successful in getting into the top six
Meanwhile, Dwight Yorke and Andy Cole told The Footballers' Football Show that Moyes was the ideal choice as United boss and not Jose Mourinho.
Former Old Trafford striking heroes Yorke and Cole backed the appointment, insisting that Moyes' managerial style and longevity at Everton had marked him out as the perfect successor to Ferguson.
Indeed, Yorke insisted that Moyes was a better fit for United than Real Madrid supremo Mourinho, claiming the Portuguese tactician's short-stay mentality would not work at Old Trafford.
"Jose is a very successful man and of course a successful manager as well, but Moyes just seems to fit and has longevity," said Yorke.
"Jose moves around and gets the best out of his players; couple of years, two or three years and then moves on. That seems to be his style of management. But at Manchester United it's a longevity job, it's not a quick fix."