The double world champion has the full approval and support of McLaren and engine partner Honda, who are having a difficult season in Formula 1.
Alonso, 35, will race for the Honda-powered Andretti team on 28 May, and the car will be branded a McLaren.
McLaren are yet to decide who will replace him in Monaco that weekend,
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The 2009 world champion has retired from F1 but is contracted to McLaren as an ambassador. It is not known whether the Briton would want to come back to drive an uncompetitive car.
Why does Alonso want to race at Indy?
Alonso said he had long held an ambition to win the so-called 'triple crown' of Monaco, the Indy 500 and Le Mans.
Only one man has won all three in his career - the late Graham Hill in the 1960s.
Alonso, who won the Monaco Grand Prix in 2006 and 2007, said: "It's a tough challenge,
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"I don't know when I'm going to race at Le Mans, but one day I intend to. I'm only 35. I've got plenty of time for that."
The Spaniard added he would definitely race for McLaren for the rest of the season, dismissing speculation he could quit part way through the year because of the Honda F1 engine's poor performance.
"It's of course a regret that I won't be able to race at Monaco this year," he said. "But Monaco will be the only 2017 grand prix I'll be missing, and I'll be back in the cockpit for the Canadian Grand Prix in Montreal in early June.
"I've never raced an IndyCar car before, and neither have I ever driven on a super-speedway, but I'm confident I'll get to grips with it fast.
"I've watched a lot of IndyCar action on TV and online, and it's clear that great precision is required to race in close proximity with other cars on the far side of 220mph [354km/h]."
Alonso acknowledged he would be on "a steep learning curve".
But he added: "I'll be flying to Indianapolis from Barcelona immediately after the Spanish Grand Prix,
Authentic Dennis Rodman Youth Jersey practising our McLaren-Honda-Andretti car at Indy from 15 May onwards, hopefully clocking up a large number of miles every day, and I know how good the Andretti Autosport guys are.
"I'll be proud to race with them, and I intend to mine their knowledge and expertise for as much information as I possibly can."
McLaren have supported Alonso's wishes because they recognise the efforts he has been putting in - and the frustration he is feeling - after three uncompetitive seasons since joining the team in 2015.
McLaren executive director Zak Brown said: "Could Fernando win this year's Indy 500? Well, I wouldn't be so silly as to make any such rash prediction,
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"Put it this way: the team he'll be racing for won the race last year, using the same Honda engine, and he's the best racing driver in the world. That's quite a compelling combination.
"He'll have his work cut out to acclimatise to running at super-speedway velocities, but ultimately it's quality that counts in all forms of motorsport, and Fernando is very definitely quality. He's ballsy and brave too."
Alonso joined McLaren-Honda with the intention of winning a third world title, but the package has been uncompetitive, with the vast majority of the blame lying with the Honda engine. His best results have been three fifth places
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