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Spalletti, who had a contract until 2021, led Inter into the Champions League for the first time in six years in the first of his two seasons.
This year his side finished fourth in Serie A and were knocked out of the Champions League at the group stage.
Conte has been out of the game since being dismissed by Chelsea last July.
Inter secured a Champions League spot on the last day of the season by beating 2-1 on Sunday to finish level on points with third-placed Atalanta.