Union paid a reported club record fee of 15 million euros for Gosens, who has signed a five-year deal, local media said. The length of the contract was not given.
Gosens arrived at Inter in January 2022 from fellow Serie A side Atalanta on loan until the end of the season before joining the 19-time Italian champions on a permanent deal.
He helped Inter to two Italian Cups and an Italian Super Cup as well as the runners-up spot in the 2022/23 Champions League.
"I've always said it's my dream to play in Germany and the Bundesliga one day," Gosens told the club website.
"Union's last few years have been impressive, and you could see that abroad too. I felt a lot of appreciation and trust in the talks with the club's executives, so the decision wasn't difficult for me."
Union finished fourth in the Bundesliga last season to qualify for their first Champions League campaign.
Gosens made his Germany debut in September 2020 in a Nations League draw against Spain. He was then included in the squad for Euro 2020, postponed by a year due to the COVID-19 pandemic, where they were knocked out by England in the last 16.
