Giampiero Ventura has left his position at Torino amid reports he will replace Antonio Conte as Italy coach after Euro 2016, while Sinisa Mihajlovic has taken over at Stadio Olimpico.
Ventura is considered to be the frontrunner to take charge of the national team following the European Championship in France, with Conte departing for Chelsea.
The 68-year-old previously played down talk of him assuming the Italy role, but the likelihood of it occurring has increased, with Mihajlovic - sacked last season by AC Milan - replacing him in Turin.
"President Urbano Cairo wishes to thank Giampiero Ventura for the great work done together and for the excellent results obtained in this rich experience of mutual satisfaction," Torino said in a statement.
"The ascent continues, enriched by the unforgettable pages to the recent history of Turin: the seventh place in Serie A, the qualification to Europe after 20 years and the first victory of an Italian team in Bilbao.
"It has been five wonderful years. Torino hope for the fortune Giampiero Ventura deserves in the continuation of his career."
Mihajlovic was dismissed by Milan in April, despite the club remaining in contention to qualify for European football and having secured a place in the Coppa Italia final.
On Monday, the Rossoneri confirmed his contract would be terminated in June, freeing him up for the move to Turin.
"I want to thank president Cairo and all of Torino for the trust placed in me," Mihajlovic said in a statement.
"Being able to work in a club with as glorious a history as Torino is a source of great pride for me."