The player was on Tyneside on Tuesday afternoon for a medical and Newcastle have agreed a fee with his club Gent.
Sels - who was voted Belgium's goalkeeper of the season for 2015/16 - was being monitored by a number of Premier League clubs.
He will become the fifth goalkeeper on Newcastle's books, joining Tim Krul, Rob Elliot, Karl Darlow and Freddie Woodman.
Sky sources understand Crystal Palace are interested in signing Krul, who is just back from a serious knee injury.
Newcastle's players reported for their first day of pre-season training on Tuesday ahead of their Sky Bet Championship campaign.