The 36-year-old had presided over Spurs for 18 months only for the club to confirm the "termination of his services" on their official website, a day after their 5-0 home defeat by Liverpool.
The humiliation by Liverpool, which followed a 6-0 drubbing by Manchester City last month, appears to have been the final straw for Spurs chairman Daniel Levy, who delivered the news in person at the club's training ground in Enfield.
Lord Sugar, who has been a prominent critic of Villas-Boas on Twitter, told ITV1: "The fact is he's gone.
"With the greatest respect to the chairman I think it was the wrong move to appoint him. I think the guy showed he was unprofessional in spending that amount of money."
Redknapp, whose dad Harry was sacked last summer to make way for Villas-Boas, told Sky Sports News: "After the job he did at Chelsea he was incredibly lucky to get that job in the first place.
"He had a nightmare at Chelsea and then they went and won the Champions League without him, but he finds himself as the manager of Tottenham with a squad of Modric, Bale and players like that.
"Last year he did well with the previous manager's team, but now he's had his chance to do it, it hasn't worked out for him.
"When you get beat 5-0 at home it's a bit of a tell-tale sign. It's not something Tottenham fans are accustomed to and I feel sorry to a certain extent for the fans.
"Having seen the team that was built - you look at Gareth Bale on the wing - and you've ended up with players who aren't in the same league."
Sugar had become something of a nemesis for Villas-Boas in recent weeks, who had accused the businessman of driving an "agenda" against him.
Sugar was unrepentant, telling Sky Sports News: "The writing was on the wall as far as I was concerned when he went out and spent like a a kid in a sweet shop, I mean you just can't do that.
"It doesn't stack up, you just can't go out and buy seven brand new players or whatever it was, stick them in and hope for them to play.
"It showed immaturity."
Manchester City boss Manuel Pellegrini felt Villas-Boas was harshly treated.
He said: "He didn't have time in both clubs but I am absolutely sure he will continue his career."
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