For McLaren, the occasion will mark the team's return to the Indy 500 after 38 years.
"Seeing the interest from a Formula One champion, a double world champion, is actually exciting, super exciting from a driver's standpoint", Simon Pagenaud said.
McLaren's lead driver Alonso will not take his seat in the F1 vehicle for the race in Monte Carlo, as instead, he will join the Andretti team in the IndyCar series, and race in one of the most prestigious events in world motor sport.
The oval race coincides with F1's equally fabled Monaco grand prix, and recently retired Button - who has a McLaren contract this year - seems the obvious choice to replace Alonso.
"It's a dream come true, the Indy 500, what a race to enter in the U.S. and hopefully win it or try to win it", Alonso said on Twitter.
The Andretti auto that Alonso will drive in the race on May 28 will be branded a McLaren, in what could be their first foray into the American motor racing series.
The 2005 and 2006 Formula One champion said he wanted to compete in the Indy 500 to have a chance of fulfilling a career ambition of completing motorsport's "Triple Crown" in winning the Monaco Grand Prix, the Indy 500 and the Le Mans 24 Hours.
"I've won the Monaco Grand Prix twice, and it's one of my ambitions to win the Triple Crown". The 101st Indy 500 race and the Monaco GP have been scheduled on the same day i.e.
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UN Special Envoy for Syria Staffan de Mistura speaks during a news conference after addressing the U.N. Security Council 's meeting on Syria, Wednesday April 12, 2017 at U.N. headquarters.
Honda is the supplier of McLaren's power units in Formula One and is one of the key reasons for the team's poor performance in the current season, and recent past ones.
"The experience that he has in motorsport, I don't think it'll be any problem for him", three-time Indianapolis 500 victor Helio Castroneves said.
Button, a veteran of more than 300 grands prix, is under contract with McLaren and could be called upon, while British driver Lando Norris, 17, was signed to the team's young driver programme earlier this year.
Alonso, who has 32 grand prix victories, is competing in his 15th season in F1.
The only driver to win a Formula One title and then win the Indianapolis 500 in his first attempt was Graham Hill - in 1966, four years after the first of his two F1 titles.
"Monaco will be the only 2017 Grand Prix I'll be missing, and I'll be back in the cockpit of the McLaren-Honda for the Canadian Grand Prix in Montreal in early June", he said. "Well, I wouldn't be so silly as to make any such rash prediction, but I expect him to be in the mix".
McLaren won the Indianapolis 500 with their own auto in 1974 and 1976, but IndyCar is now a "spec" formula where all teams use the same basic vehicle, although different engine manufacturers are allowed to design their own aerodynamic bodykits.
Nine rookie drivers have won the Indy 500, including Alexander Rossi at last year's race.
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