The 22-year-old was a free agent after his contract with Schalke expired at the end of last season.
Meyer becomes the Eagles third signing of the summer and will wear the number 7 shirt.
"I feel really good and I'm happy to be here," said Meyer. “I can't wait to start training with the team and I hope I'll have a good season.
"I'm proud to be here and I hope I can make the next step in my career. I want to give my best and I think we can have a good season - maybe better than the last.
"I played at Selhurst Park last season for Schalke and the atmosphere was perfect, and I can't wait to experience the atmosphere for a Premier League game."
Introducing the new #MeyerOfLondon... pic.twitter.com/rnSi32iWDp
— Crystal Palace F.C. (@CPFC) August 2, 2018