The England Defender will undergo a medical for a two-and-a-half-year contract with the option of a further year.
Newcastle and Atletico reached a deal to sign the player on Tuesday.
Sky sports reported that the club will pay £12m plus add-ons to make the 31-year-old the first signing of the new Newcastle era under the Saudi Arabia owners.
Atletico wanted Trippier to stay, but the defender made it clear he wanted to return home.
Newcastle manager Eddie Howe worked with Trippier while in charge of Burnley, signing the right-back from Manchester City in January 2012 after an impressive loan spell.
Newcastle’s owners hope to recruit at least three more players this month as they look to keep the club in the Premier League.