Tottenham chairman Daniel Levy took a huge gamble on Monday night when he named Sherwood as the club's new manager.
The 44-year-old, who has been given an 18-month contract, has very limited experience when it comes to management.
Sherwood has coached Spurs' development side, but his only two games in charge of the first team came when Levy sacked Villas-Boas and asked the former Tottenham midfielder to take over on a temporary basis.
But Redknapp, who first brought Sherwood to the club in 2008, is sure the former England and Blackburn man will be a success.
"They've made a great decision to give him the job," the former Spurs manager told talkSPORT.
"Villas-Boas was a scout for years and years. He never played football.
"He got thrown into the deep end, did a great job at Porto, and got the Chelsea and Tottenham job off the back of that.
"Tim has far more football experience than the previous manager had. He's been a top player and captained Blackburn. He's been coaching for many years with the Under-21s so he's not short of experience.
"He's got no fear and can handle players. He won't be afraid of talking to them because they were bought for £20-30million, it will make no difference to him."
Sherwood took up a part-time coaching role at Spurs under Redknapp in 2008 before moving up the ladder to become technical co-ordinator.
Redknapp saw promise in Sherwood during his three-year spell at Spurs and made sure the new manager was exposed to as much experience of first-team affairs as possible.
"When I was there he travelled to every first-team game with me, including all the away European games," Redknapp added.
"He'd come and watch the first-team games every Saturday after training the kids on a Saturday. So he's been around the first team for a good few years."
Sherwood won his first Barclays Premier League game last Sunday when Spurs came from behind to register an impressive 3-2 win at Southampton.
Tottenham now sit four points off the top four but victories over West Brom and Stoke in the coming days can put the team firmly back in contention.
Redknapp took Spurs into the Champions League in 2010 and the QPR manager thinks Sherwood can achieve the same feat this year.
Redknapp even believes that Tottenham can catch second-place Arsenal, who have spent much of the season at the top of the Barclays Premier League.
"I thought Tottenham were absolute certainties to finish above Arsenal at the start of the season," Redknapp said.
"Then Arsenal lost their first game of the season, but they have done fantastic since then. But they are only six points above Tottenham.
"That's nothing. That can be wiped out in a week, so Tottenham are still bang in there.
"They have a good squad. I think Tim will get the best out of them. I wouldn't write Tottenham off four a top-four position, they have got as good a chance as the seven teams that will be scrapping it out until the end of the season."
Sherwood is expected to be without winger Aaron Lennon, who has an abdominal injury, for his first full game in charge against the Baggies on Boxing Day.
The new boss does have midfielder Mousa Dembele available though, after he recovered from an ankle injury he suffered at St Mary's last weekend.