The 34-year-old manager had been out of work since his sacking by the west London club in March but was appointed as Harry Redknapp's successor on a three-year deal on Tuesday.
And Lampard, who clashed with the Portuguese during his time at Stamford Bridge, says Villas-Boas has a tough act to follow in north London.
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“AVB has inherited an exceptional squad of players," he told The Sun.
“A squad that’s good enough to bring Champions League football and contend for the Premier League title. A team that’s played some terrific, thrilling attacking football and scored goals for fun.
“So AVB is a lucky man taking over at Spurs because the players are so very good. Admittedly that can be a double-edged sword, though.
“Because Harry Redknapp will be an extremely tough act to follow. Harry lifted Spurs to an amazing level.
“The way he turned that club around was remarkable. They were at absolute rock bottom when Harry came in.
“Then all of a sudden they’re playing in the Champions League and competing at the very top. So he did an incredible job there and he definitely didn’t deserve to lose his job.
“That’s why I was really surprised when Harry left. He did wonders at Tottenham and I thought him leaving was a terrible shame.”
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The 33-year-old also expressed his belief that Villas-Boas will have improved as a manager by learning from his disastrous spell at Chelsea.
“AVB didn’t do well at Chelsea but it was not for the want of anyone trying," he continued.
“He wanted to succeed, he wanted to do it his way. But it just didn’t work. Not because of any battle between me and him, there was a lot more to it than that.
“He had his plans for the team and that meant me not playing as much as before. That was just one part of it, the problems were far bigger and broader than that.
“But as a player you learn off every manager whether they are good, bad or indifferent. I definitely learned in different ways from Andre. It was an interesting time.
“I was always used to having a great relationship with my managers. Everyone I had worked previously with.
“Not having that suddenly made it pretty tough for me at the time. It makes you stop and think, it makes you re-evaluate everything you are doing.
“That’s not necessarily a bad thing. Now maybe he will be a better manager, a better person for his experience at Chelsea.”
The England international went on to reveal that he is looking forward to coming up against his former boss when the two London sides meet in the Premier League.
“Yes, AVB now being at Spurs will give those derby games even more of an edge," he said.
“They are pretty edgy anyway but this will add even more. When I see him I’ll shake his hand and wish him all the best. But then I will try my best to beat him.”