Villas-Boas is the seventh boss of the Roman Abramovich era, but Buck believes the club may finally have found their Sir Alex Ferguson figure.
Ferguson will celebrate 25 years in charge of United next month, while Arsene Wenger last week marked 15 years as Arsenal manager.
Buck told BBC Sport: "We do envy Arsene Wenger at Arsenal and Sir Alex Ferguson at Manchester United in terms of longevity, but it shouldn't be longevity for longevity's sake.
"It has to be the right guy in the job for 10 or 15 years and, in light of Andre's age, he may well be that guy."
Villas-Boas turns 34 this month and is only his third season of full-time management.
The Portuguese has previously said he only wants to remain in the profession for between 10 and 15 years.
Buck added: "Everyone thinks his age might have been a negative but it's a positive.
"He has really been able to relate to the players. He is a very organised guy who really understands football."
Buck this week announced Chelsea's plan to buy back the parts of Stamford Bridge they do not already own in what is being seen as a precursor to a stadium move that could earn the club an extra £50million per year.
He also admitted they need to improve their youth development policy to make further savings in the light of UEFA's Financial Fair Play regulations.
"The problem has been transfer fees paid to other clubs for new players and that's probably our biggest expense," he said.
"The way we've tried to attack that - not as successfully as we'd have liked to be honest - is by putting a lot of money into the academy.
"The maths is pretty simple. If you can bring a player or two through the academy every couple of years, then you're saving £10million, £20million, £30million of transfer fees."