The 19-year-old has been at Peterborough for seven years, having arrived at the club's academy at the age of 12. The Portuguese midfielder has made 108 appearances in all competitions for the League One side, after making his senior debut at the age of 16.
Speaking after Wigan signed Da Silva Lopes, 'Latics' boss Paul Cook said that the young player has a lot of potential.
"Leo has been one of the best young players in the EFL over the past couple of seasons, this is a really strong addition to our squad," he said.
"I am looking forward to working with Leo and believe he will embrace the challenge of Championship football here at Wigan Athletic.
"Everyone has to remember Leo is just 19 and has his best years ahead of him but he certainly has the foundations to become a top level player.
"Thanks to the Chairman for his work in getting this deal completed so early in the window, which will give Leo the chance to come in and work with us straight away in pre-season."