The two showpiece races take place on May 28 and McLaren - whose fortunes have plummeted in F1 - "will enter a single vehicle in the 101st Indianapolis 500", said a team statement.
The British outfit had announced earlier this week that Alonso would be participating in the Indianapolis 500 series for a single race on 28th May 2017.
On the back of two uncompetitive seasons at Mclaren and facing a hard third ahead, Alonso, 35, is said to be looking to achieve the "triple crown", becoming a victor of Monaco, Indy 500, and Le Mans.
Towards the end of last season, Jenson Button confirmed that he would not be racing in Formula One for 2017, with Stoffel Vandoorne being promoted to the second seat. "His vehicle is going to run with some guy everybody will be pretty familiar with".
Alonso has just over six weeks until he lines up at the Indianapolis Motor Speedway, during which time he will compete in three races - including this weekend's Bahrain Grand Prix.
Boullier reportedly said when he called Button to discuss the situation, the 37-year-old immediately responded "great, I'm so excited", and his eagerness was palpable. "It will be hard if we can't".
"I realise I'll be on a steep learning curve, but I'll be flying to Indianapolis from Barcelona immediately after the Spanish Grand Prix", said Alonso.
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F1 drivers up and down the paddock spent much of the off-season in gruelling training camps in preparation for the high-downforce conditions that come along with new regulations.
He said: "I wouldn't miss out any of the races in F1, definitely continue to do all the races".
"I like Jenson and I think he's one of the best drivers".
"On the planes I will try and look at some videos and races from the last years. Ferrari have shown tremendous pace and at the first race in Australia in race trim they were very quick - particularly on a hot circuit - so the gap is going to be even closer here". After all, he's missed only a handful of races since Abu Dhabi a year ago, and he's as fit as a fiddle. "It's good if that's what he wants to do but honestly I'm surprised that it's happening", said Grosjean.
Outside of Button, the options for McLaren appear slim. "So I think he needs to see a psychiatrist, personally".
But although many within the sport have welcomed the idea of Alonso racing in America, Horner thinks that Brown needs to see a "psychiatrist" for letting his driver compete at Indy.
The Briton has raced in Monaco 15 times during his career, winning during his championship season in 2009.