The 31-year-old is Newcastle's first signing under their new Saudi owners and their first since Eddie Howe was appointed manager in November.
"I'm delighted to be joining this fantastic club," said Trippier, who has agreed a deal until the end of the 2023-24 season.
Howe also signed Trippier in 2012 during his time as Burnley boss.
Trippier, who helped Diego Simeone's side win the Spanish title last season, had 18 months left on his contract.
Newcastle are second bottom of the Premier League, having won one league game this season.
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