The former world champion took a sabbatical from the sport at the end of last season and was replaced by 2015 GP2 champion Stoffel Vandoorne.
Although Button's role is defined as ambassadorial, he is contracted to the team until the end of 2018 and is still eligible to drive.
The Italian's decision to miss the race in Monte Carlo on May 28th has raised some eyebrows and given weight to the suggestion that the former Ferrari driver has become increasingly disappointed with the performance of the car, in particular the Honda engine.
It has been a disappointing start to the season for the British team who have failed to pick up any points from the first two races in Australia and China.
However, a familiar face will be returning to the cockpit in 37-year-old Button. He said of his return: "I'm thrilled to be making a one-off return to Formula One racing, and I couldn't think of a better place to make that return than my adopted home Grand Prix: Monaco.
"It's a tricky street circuit on which a good driver can really make a difference - and, although the McLaren-Honda MCL32 hasn't begun the season well, I think it may be more suited to Monaco than to the faster circuits that Fernando and Stoffel have raced it on so far this season."
Alonso is not the first Formula 1 driver to take on the Indy challenge, with Jim Clark, Graham Hill and Jacques Villeneuve among those who have won the annual competition.
McLaren's racing director Eric Boullier said Button was the obvious choice to replace Alonso, who has opted to compete in this year's Indianapolis 500 as part of a potential bid for motorsport's historic triple crown - a feat only Graham Hill has ever achieved.
Should he lift the title in America, he would need to win the legendary Le Mans race which runs in the French city ever June. The 35-year-old has suggested he will compete in the competition once he has retired from F1.
"I was truly delighted when Jenson accepted our suggestion that he race at Monaco instead of Fernando.
"Jenson is a class act. He's a superb driver - fast, smooth and precise - and he won't have lost any of his competitive edge over the past few months. After all, he's missed only a handful of grands prix since his last outing in Abu Dhabi in late November last year, and he's as fit as a fiddle.
"Also, he's always been good at Monaco. He'll do a great job for us, I'm sure of that."
Button won at the Circuit de Monaco in 2009 ahead of lifting the driver's title, and will feel confident of picking up points ahead of the race at a track that is suited to the slower pace of the McLaren-Honda car.