Anita, 28, whose deal at St James' Park was not renewed by Rafael Benitez at the end of the season, has agreed a three-year contract with Leeds and is head coach Thomas Christiansen's sixth summer signing.
"Leeds United are delighted to confirm that Dutch international ace Vurnon Anita has secured a three-year contract with the Whites from Premier League side Newcastle United," the Sky Bet Championship club announced on their official website.
"The defensive midfielder becomes the club's sixth signing of the summer after securing deals with Felix Wiedwald, Mateusz Klich, Hadi Sacko, Pontus Jansson and Madger Gomes."
Anita, who operated as a central defensive midfielder or at full-back during his five-year spell at Newcastle, made over 150 appearances in total after joining from Ajax for a reported B£6.7million in August 2012.
The former Holland international, who had progressed through Ajax's youth system, made 27 Championship appearances last season as Newcastle won promotion back to the Premier League.
Leeds have signed Klich, Gomes and goalkeeper Wiedwald since the end of the season and have turned the loan spells of Sacko and Jansson into permanent deals.