According to Fabrizio Romano, the 26-year-old is now a fully-fledged Juventus player after the obligation to buy was activated.
Kelly joined the Italian giants from Newcastle on loan in January, just six-months after he was signed as a free agent from Bournemouth.
Juventus will pay a fee of €17.5m plus add-ons for Kelly, who has made 13 appearances across all competitions for the Serie A side.
Like Newcastle, Juve are fighting to qualify for next season’s Champions League, sitting in fourth in the Italian top flight with three games remaining.