The 27-year-old Spanish full-back had been in talks with Fulham but Chris Hughton has persuaded him to move to the south coast.
Montoya, 27, signed for Valencia in 2016 and has made 52 appearances for the club, scoring twice.
It is understood that Montoya believes that he will get more game time at Brighton, as the Spaniard will compete with Ezequiel Schelotto and veteran Brighton captain Bruno Saltor for a place in Hughton's starting XI.
It is understood that Valencia are unwilling to sell Montoya permanently, however a season-long loan has been agreed by with clubs.
He has represented Spain at youth levels, from U17 through to U23, but has not made a senior appearance.
Montoya joined Valencia from Barcelona in 2016.
Southampton are also rumoured to be interested in the 27-year-old's services.
Brighton hope to complete the signing before the transfer window closes for British clubs at 5pm BST.