Vaughan, who famously led England to their surprise 2005 Ashes series victory but quit the captain's post himself after a loss of batting form last August, senses a "decent man" like Strauss fits the bill at a critical time.
With the Ashes looming and a Test series set to begin in the West Indies next month, England landed two major self-inflicted blows yesterday when Pietersen resigned after just three Tests in charge and coach Peter Moores - whose disintegrating relationship with the captain caused the crisis - was sacked.
Vaughan himself, left out of the Caribbean tour after a lack of opportunity to regain his form this winter, was being touted by some to return to lead England until strong favourite Strauss was named last night.
The Ashes-winning captain is in no doubt the England and Wales Cricket Board have chosen wisely.
"If there is one man who can get the England team to gel and bring the players together after weeks or even months of damaging rumours, it is Andrew Strauss," Vaughan writes in his Daily Telegraph column.
"In the 18 months since Peter Moores took over as coach the results have not been good - but I think Strauss will be a very, very good captain.
"Such a decent man can bring back maturity and stability to the England team."
Vaughan's omission from the squad to face the West Indies was reportedly the issue which pushed Pietersen and Moores' disagreements to an unworkable level.
Pietersen is thought to have wanted his old captain back in the ranks - a policy resisted by the selectors in his absence.
Vaughan still hopes that somehow yesterday's drama can help England move forward.
"It may be that everything happens for a reason and things will turn out the best for English cricket," he added.
His mission, meanwhile, for Pietersen - should he choose to accept it - is simple.
"What Kevin has to do now is go to the West Indies and score a hundred in the first Test - then all the controversy will be forgotten," Vaughan prescribes.
"KP is very much his own person, which shows in his batting. He has never used a batting coach; he relies on his natural flair; he does it his own way - like the maverick he is. That is the genius he is.
"He is the one England player I have played with who has the ability to sustain that number one position in the world. He is that good. That now has to be his goal."
As for his own future, Vaughan took the opportunity to rule out any fanciful notions that he could be considered for the coaching role vacated by Moores and thought most likely to fall - on an interim basis at least - to Andy Flower.
"Finally I'd like to add that I'm not interested in coaching England or anyone else at the moment," he spells out.
"I want to play and score hundreds for Yorkshire and England again."
Duncan Fletcher, the England coach who helped Vaughan's team win the Ashes four years ago, fears there will be tricky times ahead for Strauss.
Fletcher left his post after England's hopes of defending the Ashes ended instead in a 5-0 whitewash Down Under - and then an early elimination from a troubled 2007 World Cup compounded matters.
He is astounded the ECB were unable to limit the damage of Pietersen and Moores' apparent personality clash and expects the fall-out to haunt England, leaving Strauss with more fire-fighting ahead.
"What a mess," Fletcher exclaims in the Guardian.
"How sad for English cricket that a year containing a home Ashes series has begun in such chaos."
It is the future, though, which concerns Fletcher most - and he warns Strauss is highly likely to be put in an uncomfortable and unenviable position.
"The selectors really should have stepped in before things turned ugly. Instead, England are in real trouble with the arrival of the Australians only a few months away. It all seems such a shame."
Fletcher believes Strauss, expected to lead England on the one-day leg as well as in the Tests in the Caribbean - despite his perceived ineffectiveness as a limited-overs batsman - may find himself trying to unite divided factions within the team.
"Andrew Strauss was the only viable option. But he will need the support of all the other players, and he will need to be rated by the other players too - which is crucial for any leader," he explains.
"There are egos in that dressing room who could cause more problems for the new captain. Not least of the difficulties will be how to handle KP when he returns to the rank and file.
"The ECB has exposed him somewhat by admitting that its research, whatever form it took, revealed a lack of support for Pietersen as captain.
"That to me sounds like a huge problem in the making: will the dressing room divide into pro- and anti-KP camps?
"Will the new captain have the backing of all the senior players? It's going to be a huge issue for the poor captain in the months ahead."
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