Yanga-Mbiwa arrived at Rome's Fiumicino Airport on Monday and is reportedly undergoing a medical before completing his Serie A switch.
"I am happy, forza Roma," Yanga-Mbiwa was reported as saying by the Italian press.
The 25-year-old was looking to leave the Magpies this summer after finding himself down the pecking order under manager Alan Pardew.
The France international moved to St James' Park in January 2013 from Ligue 1 side Montpellier.
Yanga-Mbiwa is under contract with Newcastle for another four years.
A move to Roma, who won their Serie A opener 2-0 against Fiorentina on Saturday, will allow Yanga-Mbiwa to play Champions League football.
Roma finished runners-up in Italy's top flight last season and will face Manchester City, Bayern Munich and CSKA Moscow in the group stages of Europe's elite club competition.
- Sports & Recreation
- Fiumicino Airport