Woods and Mickelson were joined by 1992 champion Fred Couples and Belgium’s Thomas Pieters as they teed off from the 10th shortly after 08:30 local time on Tuesday.
Mickelson, 47, who won for the first time since 2013 last month, is aiming to surpass Jack Nicklaus as the oldest ever winner at Augusta National.
And Woods, who underwent spinal fusion surgery last April, is seeking a first major title – and 15th in total – since winning the US Open in 2008.
With both men due to hold their pre-tournament press conference on Tuesday afternoon, it was expected that they would only play the back nine.
European Ryder Cup captain Thomas Bjorn has said that having a rejuvenated Tiger Woods playing in September for the Americans against his team in Paris would be a “massive bonus” for golf.
Fourteen-time major champion Woods has impressed since returning to the PGA Tour after a series of injury problems, notching back-to-back top-five finishes for the first time since 2013.
Bjorn insisted that he wouldn’t be disappointed if his players have to face up against the former world number one, saying a fit and firing Tiger at the Ryder Cup would be “unbelievable for the game”.
“Tiger Woods’ involvement for the game of golf is hugely important,” Dane Bjorn told AFP.
“He is the ultimate superstar in sport and that’s very important for the game that he’s involved.
“I think it’ll be great for the game if he (Woods) plays and a massive bonus for the Ryder Cup in France. If he got back to a place where he was among the best 12 players in America… I think for the game of golf that would be unbelievable.”
Woods will head into the Masters next month as one of the favourites for the green jacket, a remarkable situation given he was ranked outside of the world’s top 1,000 just last year.
The 42-year-old, a veteran of seven Ryder Cups, has only been part of one winning American side — back in 1999.
But Bjorn warned against underestimating “the best that’s ever played”.
“Now that he’s back on the golf course and playing well, once he starts getting confident he’s the best that’s ever played and he can do incredible things,” he added.
“It will be interesting to see how the next three or four months develop in Tiger Woods’ golf life, because there seems to be the thing about him that’s a bit more humble.
“I think he’s really happy with the way things have developed and I think he’ll go and do really good things.”
Woods, who will be hoping to claim an 80th PGA Tour title in the coming months, has already been appointed as a vice-captain to US skipper Jim Furyk for the matches in France.
But Bjorn knows that having an in-form Woods playing instead of on the sidelines would be anything but a boost for Europe’s chances of regaining the trophy.
“He can play himself into the team and then the vice-captaincy disappears a little bit because he has to focus on his playing,” said Bjorn.
“But America have a very good set-up now with Jim (Furyk) being captain and guys like Davis Love and Steve Stricker.
They’ve been around a long time and they know each other very well.”
With Dustin Johnson and Justin Thomas fighting it out for the world no. 1 spot and the likes of Phil Mickelson and Patrick Reed hitting form, the addition of Woods could make an already-formidable American line-up look even stronger at Le Golf National in six months’ time.
Tiger Woods’ comeback is not only good for the game of golf, but also for business, PGA Tour commissioner Jay Monahan has claimed.
The 42-year-old 14-time major champion recently finished second at Valspar, in a telling performance just a few weeks before next month’s Masters at Augusta.
“It’s a story that the world is finding very compelling and… That’s what you want as a business,” PGA Tour commissioner Monahan told CNN.
NBC Sports reported its third-round TV viewing figures on the Golf Channel were up 181% on the same day last year, while the final round drew a 5.11 overnight rating – the highest audience outside the majors since the 2013 Players Championship, won by Woods.
What followed was the highest non-Masters ratings since the 2015 PGA Championship, despite the emergence of exciting new American stars such as Jordan Spieth during that period.
Alongside audience figures, Monahan also outlines to CNN what he believes draws people in to Woods’ comeback, and whether it can be sustained.