The transfer fee of £69m is the highest amount the club has ever paid for a player, surpassing the £63m spent on Alexander Isak from Real Sociedad.
Woltemade, 23, will replace Isak, who is set to join Liverpool.
He has signed a contract with Newcastle until 2031 and expressed his excitement about joining the club.
"I'm really happy to be at this amazing club," Woltemade said. "From the first contact, I felt like the club really wanted me and had big plans for me.
"It's a big step in my life to leave Germany, but everyone has welcomed me so well, and it already feels like family."
Newcastle manager Eddie Howe is pleased to have Woltemade on board, saying he fits the club's profile for attacking options.
"He's strong in many areas, with great technical ability and a proven track record in a top European league," Howe said.
"He's still young and has room to grow and develop here."