"I'd be surprised if he doesn't win at least six majors," former world number one McEnroe told BBC Sport.
"He's come into his own and there's a lot to look forward to."
McEnroe on Murray
"Murray has a two, three, four-year period - a couple of years especially - where he's going to be tough to beat, really tough."
Murray came away from his first 27 Grand Slam tournaments empty-handed, but has now won two in the space of 10 months.
lost to Roger Federer
in last year's Wimbledon final, the Scot made amends on his eighth appearance at the All England Club.
"This is a big thing," explained seven-time Grand Slam singles champion McEnroe. "This is a new face who has stepped up in a big way.
"It's clearly important for all of tennis, but here [in Britain] it's monumental. Every year people ask the same questions - now he never has to hear Fred Perry's name again.
"When he pumped his fists at the end, I thought he was doing it to [former British number one] Tim Henman in the BBC commentary booth because he had some mutual respect for what Tim had done himself.
"But he said it was a little defiance towards the press. He's shut them down and will never have to hear people again asking whether he can win it. Hopefully he'll get the respect he deserves. He looks pretty darn good to me."
Wimbledon is Murray's second Grand Slam title after he won the 2012 US Open
It is the 36th time a British man has won the Wimbledon singles title - more than any other nation
Fred Perry was the last British man to win Wimbledon, completing a hat-trick of wins in 1936
Harold Mahony is the only other Scotsman to win the Wimbledon singles title - in 1896
Murray is the most successful British man in terms of Grand Slam match wins with 113, ahead of Perry on 106
Perry won eight Grand Slam titles - three Wimbledons, one French Open, three US Opens and one Australian Open
Murray has reached seven Grand Slam finals, behind Perry's 10
Murray, who earned a first prize of £1.6m for his win, is the only man to currently hold two of the four majors and can now focus on his defence of the US Open, which takes place between 26 August and 9 September.
Although Murray remains second in the rankings behind Djokovic, the Scot's victory on Centre Court ensured the gap is closing.
"He's got a two, three, four-year period - a couple of years especially - where he's going to be tough to beat, really tough," said McEnroe, a three-time singles champion at Wimbledon.
"He sometimes says hard courts are his favourite surface - maybe he'll beg to differ now - but he has a chance to be number one in the world this year if things go well for him.
"He could win the US Open to have two majors this year; no-one else would have that."
"It's been a long time coming," McEnroe said. "He was getting closer and, to me, the Olympics was the big difference.
"He had to get back off the mat after losing to Federer last year and that forced him to get back on the court quicker. All of a sudden the crowd really got behind him, realised they could make a difference and they did.
"He won the US Open, so that took a little bit of pressure off coming into this year's Wimbledon. The draw opened up and it was like 'he's got to get at least to the final'.
"He did that and then he was able to play up to his ability. It was very hot - a lot of strain and stress on both guys."
Djokovic, 26, took four hours and 43 minutes to beat Juan Martin del Potro in five sets on Friday to reach the final.
And McEnroe added: "I think the
Del Potro semi-final
took a bit out of Djokovic, while Murray was moving exceptionally well and made an impact that way. Novak was a little shaken at times."
Andy Murray talks to BBC Breakfast after historic Wimbledon win
suffered shock defeats in the first week of Wimbledon, but McEnroe hopes Nadal at least can return to challenge Murray and Djokovic.
"It depends with Rafa - we're all hoping he'll come back in the mix and not just on clay," added the 54-year-old American.
"There's some concern based on what happened here, but hopefully that's a blip because if we had three of them that would really be special.
"Roger is now going to be all bent out of shape and it's not easy at his age - he'll be 32 in August - to expect him to be able to go deep into a best-of-five match and stay with those younger guys.
"But then someone else is going to come along. Jerzy Janowicz showed up and there's going to be another guy, maybe him, that's going to cause problems. Del Potro was fantastic. We'll see."
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