The two-time F1 World Champion led for parts of last year’s event at the Brickyard, before being forced to retire in the closing stages.
McLaren have won the event on three previous occasions, all in the 1970s. They will return in 2019 as McLaren Racing.
CEO Zak Brown said that both the team and driver cannot wait to get back to the States and have a second crack at the Crown.
“We are relishing our return to the Brickyard and this incredible race,” Brown said.
“McLaren has a long and fond relationship with the Indianapolis 500 and it’s a case of unfinished business for us with Fernando.
“No Indy 500 is a cakewalk, it’s a massive challenge.
“We have the utmost respect for the race and our competitors. So, we are under no illusions.
“But McLaren are racers first and foremost, as is Fernando. We’re going for it.”
The Triple Crown of motor racing includes the Monaco Grand Prix, 24 Hours of Le Mans and the Indy 500.
Alonso, who leaves F1 at the end of the year, would become only the second man after Graham Hill to achieve the feat if he were to win at the Brickyard in 2019.
“I’ve made clear for some time my desire to achieve the Triple Crown,” Alonso said.
“I had an incredible experience at Indianapolis in 2017 and I knew in my heart of hearts I had to go back if the opportunity was there.
“I’m especially glad to be returning with McLaren.”
Despite the fact that he is leaving McLaren and Formula 1 after the Abu Dhabi Grand Prix, he wanted to do the Indy 500 with the team.
“This was always my first choice if the team decided to do it, so I’m delighted they’ve decided to go ahead,” he added.
“It’s a tough race and we’ll be up against the best, so it will be a huge challenge.
“But we’re racers and that’s why we race.
“One of the things I’m looking forward to most is seeing the fans again, who are absolutely fantastic.”