The transfer fee that the Championship club paid for the 20-year-old has not been disclosed, but the Trotters have stated that the youngster will initially feature for their development squad.
"I am really happy to be in Bolton," he told Bolton's official website. "It is a dream that really came true and I am very proud to be here.
"Dougie Freedman asked to see me which was a wonderful feeling. He is a great manager, so to hear that he likes the way I play is fantastic.
"It is a great opportunity for me. I met some of the players briefly and they were all very welcoming. I'm very excited to get going."
Bastos joined Differdange from US Rumelange in 2012.