Bastianini confirmed he had signed for Ducati at the San Marino Grand Prix in September.
Marini, who is Valentino Rossi's half-brother, said being given the chance to compete at the sport's highest level was a dream come true.
"Competing in MotoGP is every rider's dream," he told the motogp.com website at the European Grand Prix in Valencia.
"Having this great opportunity and being able to share it with the Sky Racing Team VR46, Esponsorama Racing and Ducati is even better. In these years with the team I have gained experience, I have grown and I have achieved the first important results.
"We are in a crucial phase of the season, we will continue to work hard to reach the maximum goal before making this big step together."
Marini's elevation means former Moto2 world champion Tito Rabat will not be on the MotoGP grid next season.
Marini is currently eight points clear of Bastianini at the top of the MotoGP feeder series. (Reporting by Simon Jennings in Bengaluru Editing by Christian Radnedge)