Track officials made the later-than-usual announcement in a news release sent out early Wednesday morning.
In a statement released by track officials, the NFL coach called the opportunity a "tremendous thrill."
Harbaugh has strong ties to the Indianapolis area. He played four seasons with the Indianapolis Colts, where he earned the nickname "Captain Comeback," and is a part-time owner of Indianapolis-based Panther Racing. JR Hildebrand, who starts 10th, and Townsend Bell, who starts 22nd, both drive for Panther.
Harbaugh led the 49ers to the NFC championship last season but lost in the Super Bowl to a Baltimore team coached by his brother, John. Harbaugh's brother-in-law is Indiana basketball coach Tom Crean.