Gosens has joined the Italian champions on loan until the end of the season and the move will be made permanent for €25m this summer.
Gosens is one of the highest scoring defenders in Europe, having struck double figures for goals from his wing-back position in each of the last two seasons.
The 27-year-old Germany international joined Atalanta from Dutch side Heracles Almelo in the summer of 2017 and made over 150 appearances for the Bergamo-based side.
He has been restricted to just eight appearances so far this season because of injury but has still chipped in with two goals.
“Over four years have passed since I arrived at Atalanta as an unknown youngster,” wrote Gosens on Instagram.
“This club gave me the opportunity to play in Serie A and the confidence to grow as a player and above all as a man. From the first minute, I gave my all for this jersey and Bergamo will always be a special city for me and my family. I had incredible experiences here, found friends for life and my son was born here too!
“So thank you to the fans who supported me always, thank you to the teammates who helped me grow in every training session, thank you to the staff who put faith in me and thank you to the club who gave me the opportunity to play in a great league.
“However, in football there are possibilities that come along only once and this is why I am very happy to sign for Inter!
“I hope you appreciated my work and my effort. Ciao, Robin.”