The Serie A champions will pay €11.8 million for the Argentine forward with an extra €6m to be paid if Juventus win the league and reach the Champions League semi-finals next season.
As revealed by Goal, Juventus have stepped up their efforts to sign the former Manchester United man after beginning formal talks with Manchester City over a potential move.
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However, while Milan have long held an interest in Tevez they have admitted they may need to sell before they can buy this summer.
Juventus, meanwhile, have also agreed terms with Gonzalo Higuain but look set to miss out on the Real Madrid man after Arsenal officials flew to Madrid to finalise a deal.
Tevez has endured a controversial time at Manchester City, since moving from rivals United in 2009.
Despite helping the club win both the Premier League and the FA Cup during his stay at the Etihad, the striker also spent five months out of the team after clashing with Roberto Mancini during a Champions League match against Bayern Munich.
The striker eventually returned to action for City and was the club's joint top goalscorer last season, with Sergio Aguero, scoring 17 goals from 47 appearances.