He has been sent to Elephant Conservation and Care Centre (ECCC) at Mathura in Uttar Pradesh, it said.
PETA had launched a campaign for rescue of Gajraj, who was kept chained near a popular temple in Aundh.
In April, Maharashtra government-appointed veterinarians confirmed that the elephant was suffering from untreated abscesses on his hindquarters and elbows, as well as a painful foot condition, PETA said.
Several celebrities, including Jacqueline Fernandez, Suniel Shetty, Sunny Leone, Sidharth Malhotra and Sonakshi Sinha had supported PETA's campaign for the animal's rescue.