The 71-year-old rocker took to social media to offer the reward for information leading to an arrest in the case and the return of the items, which were stolen from the Musonia School of Music in North Hollywood, California last month (November 2019), reports aceshowbiz.com.
Sharing photographs of the stolen instruments on Instagram, the Black Sabbath rocker wrote: "As many of you have heard, the Musonia School of Music in N. Hollywood, CA (the school where Randy Rhoads famously taught guitar) was viciously robbed on Thanksgiving night."
"Musonia was run by Randy's late mother, Delores, and after his death 37 years ago, the school became something of a pilgrimage to his fans from all over the world. It is a place where the Rhoads Family happily opened their hearts to share the life of Randy."
"As you can imagine, the items that were stolen, including Randy's first electric guitar, are irreplaceable to the Rhoads Family."
Osbourne then shared he was personally "heartbroken" over the thefts and the damage caused at the school by the trespassing thieves.
Rhoads learned to play guitar at Musonia, which is now run by his brother, Kelle Rhoads. The school also doubles up as the Randy Rhoads Museum.
The young star was killed in 1982, at the age of 25, when the small plane in which he was a passenger crashed after clipping Osbourne's tour bus in Leesburg, Florida. Two others died during the tragic incident.
( With inputs from IANS )