The 22-year-old defender enjoyed a successful loan spell at the Stade de Suisse last season, helping Adi Hütter's side to finish second in the Swiss Super League.
Mbabu has signed a three-year contract with Young Boys.
He joined Newcastle as a teenager from Servette in January 2013 and, after injuries restricted his initial progress, Steve McClaren handed him a surprise debut in a Capital One Cup defeat to Sheffield Wednesday in September 2015 before pitching him in for a Premier League bow against Chelsea three days later.
Mbabu also had a loan spell with Rangers and made a total of five appearances for the Magpies in all competitions. The club wishes him well for the future.