The 37-year-old Spaniard led 27 laps last year on his debut at The Brickyard in a Honda-powered Andretti Autosport car before retiring with an engine problem with 21 laps to go.
The 2018 Indy 500 winner, Australian Will Power, won with Chevrolet-powered Team Penske last May.
"Having Chevrolet power behind me means we're putting ourselves in the best possible position to compete at the front," said Alonso in a McLaren statement.
The double Monaco Grand Prix winner, who won the Le Mans 24 Hours with Toyota this year, left Formula One at the end of the season last month and is targeting Indianapolis as the final part of the 'Triple Crown of Motorsport'.
The late Briton Graham Hill, also a two-times Formula One champion who died in 1975, is the only one to have done it, completing the triple in 1972. (Reporting by Alan Baldwin, editing by Ian Chadband)
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