The France international moved to the Serie A outfit on a temporary basis on transfer deadline day in September.
Sunday's 1-1 draw at Fiorentina was Yanga-Mbiwa's 20th game for Roma, triggering a clause that makes his switch a full-time deal.
"Newcastle United defender Mapou Yanga-Mbiwa has completed a transfer to AS Roma after meeting a contractual condition contained in the loan agreement between the clubs," a Newcastle statement read.
"The French defender joined Roma on a loan deal in September 2014 but it has now become a permanent move."
Yanga-Mbiwa signed for Newcastle from Montpellier - where he won Ligue 1 - in 2013, and made 37 Premier League appearances for the north east club.
This season, the 25-year-old has made 14 outings in Serie A as Roma attempt to end Juventus' run of three consecutive Scudetti.
