The Manchester City cult hero has been appointed by the Clarets to replace caretaker Michael Jackson, who took over from Sean Dyche following his sacking in April.
Kompany has managed at former club side Anderlecht since leaving the Etihad in 2019, starting as a player-manager before moving onto head-coach for two years.
Now, he's been tasked with getting Burnley back into the Premier League, just as Dyche did six years ago, following the club's final-day relegation to the Championship.
And ex-Crystal Palace owner Jordan believes that the former City captain will be able to use his time as a manager abroad to help him, just like Vieira used his time in France to guide him during his first season at Palace.
"He will be in the Patrick Vieira camp of having gone and got experience," Jordan explained on Tuesday's White and Jordan show.
"I don't think Patrick Vieira's done quite as well as people think he's done because ultimately you look at it and Newcastle finished above them [Palace] in the league after a dreadful start.
"But Patrick Vieira went away, managed New York City FC, came and managed Nice, neither one of them set the world alight, but he's got a certain type of outlook."
Vieira played under iconic Premier League manager Arsene Wenger during his time at Arsenal, while Kompany was managed by legendary bosses Pep Guardiola and Manuel Pellegrini at City.
And Jordan believes Kompany's time with these legendary managers, as well as his leadership qualities, means he'll be able to get a tune out of his new side - alongside his 'better' managerial track record than Vieira.
"And having played for a certain group of managers, he will have gained and garnered a lot of experience. This guy's done the same thing," he said.
"This guy's played for the same sort of managers, this guys got a certain characteristic which is he's a leader - a leader among the elite men, he's not going to an elite football club, he's going to a Championship football club.
"But he is a leader, he's gone and done two years in the dugout and they've been relatively successful.
"They're better than what Patrick did in his little stint in Nice and New York City as I don't think American football compares in any shape or form to anything in Europe."
The former Palace chairman continued to say that despite Burnley being relegated and losing key players such as James Tarkowski and Ben Mee, Kompany has actually landed himself in a good situation.
And he also stated that the Belgian could easily follow in the footsteps of Bournemouth manager and former Premier League star, Scott Parker.
Jordan added: "But it is a task, it is an ask, but it does fly in the face of the thinking that Burnley are going to fold up shop and start being really worried about paying off debts because Vincent Kompany won't be coming there unless he's been given certain assurances.
"He is in a fortuitous position because he's landed in a side that's just dropped out of the Premier League with parachute payments, so they would be amongst the favourites to get back out of that division.
"Everyone thought that Bournemouth were going to fall off the face of the earth and never get back in the Premier League, they did."
He added: "He [Kompany] falls into the same space as Scott Parker and other people, so he's got a chance, Vincent."
Speaking following his appointment, Kompany stated he believed Burnley were the perfect fit for him at this stage in his career, too.
"Burnley Football Club is a truly historic English side and it is an honour to be appointed first-team manager," he said.
"I'm excited by the challenge ahead. I'm looking forward to getting to work with the players and creating a positive, winning team for our fans when we return to Turf Moor.
"I've been impressed by the board's vision for the club which aligns with my own and I look forward to playing my part as we enter an important season."