The 24-year-old, named in Portugal's World Cup squad, has signed for a fee quoted by British media at about 22 million pounds ($30 million).
The move will be finalised when international clearance is granted on June 9.
The right back will be reunited with Leicester manager Claude Puel, for whom he played at French club Nice.
"The atmosphere, the fans and the football of the Premier League makes it the best in the world," Pereira told the club's television channel.
Leicester, surprise champions two years ago, finished ninth in the standings after an inconsistent campaign.
(Reporting by Neville Dalton, editing by Ed Osmond)
