England defender Trippier will become the highest paid player in Newcastle's history and the first signing since their Saudi takeover.
Newcastle are paying £12million up front, plus add-ons, for the 31-year-old.
Diego Simeone and the Atletico board were reportedly desperate to keep the England international, but the lure of a Premier League return and a lucrative contract at St James Park has proved too strong.
Trippier is undoubtedly taking a risk by trading Champions League football for a relegation dogfight with Eddie Howe's beleaguered troops, who sit in 19th place and three points off safety.
Howe and Trippier have worked together before at Burnley, with Trippier's invaluable experience likely to be called upon.
Given the finances available to the Magpies after their Saudi takeover, Trippier is unlikely to be the last arrival this month.
The Premier League side reportedly had a £30million bid for Lille defender Sven Botman rejected, with James Tarkowski another reported target.