The Swiss international will spend the coming season on loan at the German side.
“I’m looking forward to the challenge and the wonderful VfB fans,” Degen told Liverpool’s website.
“I really want to make use of my chance. It’s fantastic to be working together with Christian Gross again. I had a very successful time with him in Basel.”
Stuttgart boss Christian Gross said: “I know Philipp very well and rate him highly both as a football player and as a person.
“He is a very athletic and fast player, who often looks to push forward. Philipp wants to take his chance at VfB.”