Gagliardini has broken into Giampiero Ventura's Italy squad this season, having only cemented himself in Atalanta's squad this campaign.
The move to San Siro caps a stratospheric rise for the 22-year-old, who is yet to make his senior international bow, despite being called up for recent fixtures with Liechtenstein and Germany.
Gagliardini has only played 14 games in Serie A, but he has suitably impressed Inter as they continue to overhaul their squad under new Chinese ownership.
Joao Mario, Gabriel Barbosa and Antonio Candreva were all costly imports ahead of a campaign which has seen Frank de Boer come and go in the hot seat before Stefano Pioli has steadied the ship.
"I'm delighted to be an Inter player - this is a dream come true," Gagliardini told the club's official website. "I can't wait to work with Stefano Pioli, meet my team-mates and of course wear this jersey at San Siro, in front of the Inter fans.
"I want to do my bit to help us achieve what this club deserves."
Inter are seventh in Serie A after half of the season, five points adrift of the top three and Champions League qualification.