Villas-Boas is the seventh boss of the eight-year Roman Abramovich era, with the Russian billionaire ruthlessly disposing of the 33-year-old's predecessors.
But Buck believes Chelsea may have happened upon their Sir Alex Ferguson figure in Villas-Boas, who he said had made a huge impression on Abramovich and the Blues squad.
He said: "There's a real excitement, a buzz. The players seem happy, they're jumping around. It's just a really good feeling.
"I don't know that you can put that in words."
He added of Villas-Boas: "We feel he's got excellent man-management skills, he's a very creative guy, he's a very organised guy, he's getting along well with our players.
"You were all questioning in the spring how a 33-year-old manager could deal with a 31-year-old player. The answer is he can deal with him very well.
"The board is happy, the fans are happy, and - I guess most importantly - Mr Abramovich is happy."
Villas-Boas is only in his third season of full-time club management and has already declared he only sees himself in the profession for between 10 and 15 years.
Buck hopes that time will be spent at the Blues, admitting to the BBC this morning: "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."
Buck later set out the club's expectations of the man they hired in the summer over the next four years - including his hope the 33-year-old would finally end the club's agonising wait for Champions League glory.
He said: "In three or four years' time, we expect to have a 36-year-old manager who's been with us for four years, we expect to have won a couple of trophies - preferably a big one in Europe - and of course we hope and expect to have a contented fanbase, a contented board and a contented Mr Abramovich."
He acknowledged keeping faith with a manager would help the club avoid paying the kind expensive severance packages they had been forced to in recent years.
"Longevity does have that particular advantage," Buck said.
"You only look at longevity if you have the right guy. Luckily, we think we have the right guy now."
That is significant in the advent of UEFA's Financial Fair Play Regulations, with Chelsea having reported an annual loss of £70.9million in January.
Buck said: "You've seen the kinds of losses that we've had in the last five or six years and they've been significant - I can't deny that.
"But we need to have an approach and a structure that enable us, as the Financial Fair Play rules come in slowly, to over the time period allowed comply with Financial Fair Play."
Buck admitted that would mean Chelsea spending less in the transfer market.
He said: "It has to come down as a gross number but I can't comment on - because I don't know - whether there might be a signing in the future."
Buck added: "We are looking more at increased sponsorship and a little bit at how we might be able to trim the wage bill, so it's more of a matter of a balancing act of trying to lower our expense side a little bit and raise our revenue side."