The 24-year-old moved to Goodison Park from Sligo Rovers for just £150,000, and went on to break into the Toffees’ first team in 2010 after a successful loan spell at Blackpool with whom he won promotion to the Premier League.
The Republic of Ireland international has since featured at both right-back and on the right wing, and attributes much of his success to the role of his former manager.
"I owe him an awful lot," Coleman told the Daily Mail. "He took me from a League Of Ireland team and made me into a Premier League and international footballer.
|20/1||Everton are 20/1 with BetVictor to finish in the top four next season
"He's helped the defensive side of my game. He played me in midfield for two seasons where he saw fit for me in the first couple of years and I gained a lot of experience from that. Tony Hibbert was injured at the start of the season and he saw it was the time to give me a go at right-back, I think it was the right time.
"I can only speak about my time at Everton with him and he’s been brilliant with me and I wish him the very best and hope he can have continued success at Manchester United."
Coleman believes Moyes' appointment at Old Trafford will be a success despite the new pressures the 50-year-old will face as he takes over the reigns from Sir Alex Ferguson.
"There is expectancy. We'll have to wait and see but I'm sure he wouldn't take on a job like that if he didn't believe in his own ability," Coleman continued.
"I think Alex Ferguson had a big say in who the manager would be so he must see something good in him. He has that longevity too. He's been at Everton for 10 years and that's maybe something Alex Ferguson looked at.
"He's done so well with Everton over the last 10 years, top eight every year with maybe not the budget everyone else has. He always manages to pick up good players."
Roberto Martinez has been appointed as Moyes' successor at Goodison Park, and Coleman is eager to work under the Spaniard after Ireland team-mate James McCarthy lauded the 39-year-old's impact at Wigan.
"I'm looking forward to the new manager, starting all over again, trying to impress him in pre-season, trying to do all the things right to make sure you're in his team," Coleman added.
"I spoke to James [McCarthy] about him, he always has good things to say about him. Like David Moyes with me, Martinez was brilliant with James, so he obviously has positive things to say about him."