The 24-year-old former Dynamo Dresden and Hallescher FC player featured 34 times for Greuther Furth last season.
Frank has penned a three-year deal to become Norwich's seventh signing of the summer - and second German, after fellow defender Christoph Zimmermann.
"We were searching for some improvements in defence so I'm happy," said Canaries head coach Daniel Farke.
"He's a really solid defender but also solid at building up our game. Marcel is a young guy at just 24 so has lots of potential but is also pretty experienced."
Find all the latest football transfers on our dedicated page.
Norwich City have signed centre-back Marcel Franke for an undisclosed fee from Bundesliga II club Greuther Furth.