The 19-year-old Italian will partner Jorge Navarro at the team next season, the Spaniard likewise signed through to 2020.
“I'm happy and ready to start this new adventure,” Di Giannantonio said. “Moto2 is a demanding category, and in the beginning it will take me some time to adapt, but my desire to learn is great and I'm sure the team can help me.”
The announcement signifies an all-new line-up for the team, which has fielded a pair of Speed Up SF18 bikes for MotoGP-bound Fabio Quartararo and former Moto3 champion Danny Kent this year.
Kent, who had initially joined the team on a 2018-19 deal, has already been let go, with Edgar Pons taking his place for the rest of the current campaign.
Team boss Luca Boscoscuro said: “I am really pleased to announce that Fabio Di Giannantonio will be with us for the next two seasons.
“Having Fabio at Speed Up presents us a new and exciting challenge, and we will fight together to achieve excellent results.
“Fabio is a talented young man and has what it takes to compete in Moto2.”
Di Giannantonio is in his third full Moto3 season, having finished sixth in his rookie year and fifth in the sophomore campaign.
However, it took the Italian – who sits third, 41 points behind leader Jorge Martin, in the current standings - until this year's Brno race to notch up his first lightweight-class win.
Di Giannantonio has raced for Gresini since joining the grand prix paddock, but the relationship between the rider and team owner Fausto Gresini soured amid a contractual dispute for 2019.
2019 Moto2 line-up so far:
Tech 3 KTM
Sky Racing VR46
MV Agusta Forward Racing
Angel Nieto Team
Khairul Idham Pawi
NTS RW Racing
Honda Team Asia
Fabio Di Giannantonio, Del Conca Gresini Racing Moto3
Photo by: Gold and Goose / LAT Images