The bust was restored Friday after a Tucson couple found it in a pot turned upside down in April while they were walking through a wash.
Officials said the bust that depicts the late president wearing a coat and tie was ripped clean off its granite base at Presidio Plaza in December.
No arrests have been made.
After it was found, the sculpture underwent refurbishment before its re-installation.
The bust originally was unveiled on Nov. 22, 1964, exactly one year after Kennedy's assassination. It cost $1,000 and was paid for by the Pima County Democratic party.