Dortmund, who missed out on the Bundesliga title last season after dramatically slipping up on the final matchday, needed an 88th-minute goal by Donyell Malen to beat Cologne 1-0 in their opener. Last week they managed only a 1-1 draw at VfL Bochum with their attack looking toothless for much of the game.
Fuellkrug, who passed a medical late on Thursday, topped the scorer list last season with 16 goals, the same number as Christopher Nkunku.
"Thanks to strong performances he has become a pillar in attack for the national team," said Dortmund sports director Sebastian Kehl.
"He is powerful in the air, physically present and is strong in the one-on-ones and is uncomfortable for opponents. With these abilities he has the profile we were looking for."
Fullkrug earned his first cap last year shortly before the World Cup in Qatar, where he was one of Germany's few standout performers as the team failed to progress beyond the first round.
"I was extremely happy when the offer came because the step to this club was what I was wishing for," Fuellkrug said.
"I can develop and gain new experiences. I am ready to go to help the team be as successful as possible."