The 29-year-old has been brought in on a loan deal worth €1.8m (£1.5m), with an option to buy if the loan spell proves successful, to replace Germany U-21 captain Lewis Holtby who joined Premier League side Tottenham Hotspur on Monday.
After Schalke signed Raffael from Dynamo Kiev earlier this month, Bastos becomes the second Brazilian to join the Royal Blues before January's transfer window closes.
"He is a player with international experience, has special abilities that can help us immediately, and he is also eligible for the Champions League," said Schalke's general manager Horst Heldt.
Schalke face Turkey's Galatasaray in the last 16 of the Champions League on 20 February in Istanbul. Bastos has made ten appearances for Brazil and was in the 2010 FIFA World Cup South Africa™ squad.