At just 33, Villas-Boas will be the youngest manager in the Premier League.
He will be no stranger to the senior Chelsea players, however, having worked at Stamford Bridge as a scout under Jose Mourinho.
And Grant, who was director of football at Chelsea before taking over from Mourinho in September 2007, is confident the young coach has the personality to take Chelsea forwards.
"He is a very nice guy, is intelligent, a nice person and I enjoyed being with him, even if it was for only a short time," Grant told BBC Radio 5 Live.
"Does he have the experience? No. But the authority? Time will say. I think yes.
"I know he is young, but Pep Guardiola when he went to Barcelona was young, without experience and he did a great job.
"Football is a game of results, experience is important but more important is the quality and the authority to take a team and move it forwards."
Grant added: "When I saw Porto and how the players behaved towards him, the players liked him and he had authority, so he can do it also here.
"At the end of the day, players are human beings and if they see that he has the quality to take them forwards, they will respect him."
Despite the ruthlessness of Roman Abramovich in dismissing Ancelotti, Grant maintains managers do get plenty of backing.
"Roman is a guy who says he wants results, and he gives you everything to achieve the results," said the Israeli.
"He wants it as quick as you can, and you can expect it because he has put a lot of money in.
"At the end of the day, football is a game of results, especially Chelsea."
Villas-Boas also worked under Mourinho at Inter Milan, and followed the same route to Stamford Bridge by guiding Porto to domestic and European success.
Grant, though, insists the young coach, who also spent time with the late Sir Bobby Robson when he was in Portugal, will be his own man.
"Villas-Boas will be himself," Grant said. "As a young coach, he will take some things from here, some things from there, but as far as I have heard of him from last season, he likes to keep his own personality, his own way of how he looks at football - and you can see that his team plays a little different than Mourinho."
Villas-Boas, meanwhile, insists he will bring a fresh approach to the Chelsea dressing room.
Speaking to Chelsea TV, he said: "We are very open-minded, we are open to them, to their problems and not only the problems they face on the pitch, but their problems that they face in their day-to-day life.
"We are not just managers of the game, we are people who understand the person as a whole. This is something that we feel can have a good impact."
Source: Team Talk
Source: Team Talk