The Latics have just secured a return to the Championship but manager Paul Cook has returned to League One to complete a deal for Da Silva Lopes.
The 19-year-old has already made over 100 appearances in professional football, and Cook has admitted that he is delighted to bring in the youngster.
Cook told the club's official website: "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.
"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."
On Twitter, Peterborough owner Darragh MacAnthony said that Wigan had paid "a seven-figure fee".