Villas-Boas was appointed as Blues manager this summer after guiding Porto to three major trophies last season, and the London outfit have been defeated only once in 10 games in all competitions so far this term, taking 16 points from their opening seven Premier League fixtures.
Chelsea chairman Bruce Buck last week declared the club may finally have found their Sir Alex Ferguson figure in Villas-Boas, who he claimed could end up staying with them for 15 years, and Moyes also feels the 33-year-old could be at the helm at Stamford Bridge for the long term.
Asked if he thought Villas-Boas had adapted well to the English top flight, Moyes said: "I do. He is a student of the game.
"He got the job at Porto and made it look easy, but that is because he has worked very hard.
"It is a big thing that we are all trying to get more young players in, and I think it is going to be the same with young managers.
"I think clubs are now looking for stability - like I hope we have had at Everton - and they want managers who can go the course and have longevity.
"I think the Chelsea manager certainly could do that, because he is only about half my age! He is doing great."
Moyes, whose team travel to Chelsea for Saturday's early-evening kick-off, believes the Blues are a better side under Villas-Boas than in the previous campaign.
"From what I've seen Chelsea are a better team this year than they were last year," Moyes said.
"I think a lot of people have written Chelsea off a bit - all the focus at the moment is on Manchester United and Manchester City, but I see a fresher-looking, younger team coming up at Chelsea.
"From the bits of them I have seen, I think there is an improvement and that they will go close to the Premier League (title) at the end of the season."
Everton have a good record of late at Stamford Bridge, coming away with a point from each of their last five league visits - something Moyes feels will boost his side for this evening's contest.
"I think you go into it with that positive attitude, thinking we have been here before and done it and that we don't feel out of place in these games," Moyes said.
"But you have to remember that the games have usually been incredibly tight, and it is not as if we have ever run away with it.
"We have tended to find that Chelsea have the majority of the possession, we try to stay in the game and maybe nick something - but that is because of the quality of players they have got and it is a credit to our players that in the past they have been able to do that."