Woltemade moves to Newcastle for a club record £69m fee, which eclipses the £63m paid to Real Sociedad for Alexander Isak.
Woltemade effectively is arriving to replace Isak, as Newcastle prepare to sell him to Liverpool.
The Germany international, 23, has penned a deal to 2031.
"I'm really happy to be at this amazing club," he 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 everybody has welcomed me so well and it already feels like family. I have a really good feeling from speaking to the head coach that this is the right place for me to find my best level.
"I know the stadium from watching games on television - it looks amazing and I know the atmosphere is crazy. I'm really excited to play and start scoring goals here."
Newcastle manager Eddie Howe added: "We're delighted to get Nick's signing over the line so quickly. He fits the profile for exactly what we have been looking to add to our attacking options.
"He's strong in a lot of areas - he has great technical ability and has proven himself to be a real threat in one of Europe's top leagues - but he's also still at an age where he has plenty of room to develop and grow here."