Mbuyamba, 18, put pen to paper on a three-year contract at Stamford Bridge on Thursday and will join the Premier League club's development squad ahead of the new season.
The teenager joined Barca last summer and impressed with the club's under-19 squad but his agent Carlos Barros told Voetbal International he was concerned about his client's future prospects at the club. The defender left the Camp Nou in June.
Mbuyamba came through the youth system at Dutch side MMV Maastricht and represented the Netherlands at U19 level.
Sources have told ESPN that Chelsea are edging closer to signing Kai Havertz from Bayer Leverkusen this summer.
Chelsea are also looking to bolster their options in defence with Lampard focused on signing a left-back. Leicester City defender Ben Chilwell is their top target but the club are also keeping tabs on Ajax's Nicolas Tagliafico and Real Madrid's Sergio Reguilon.
The Blues will kick off their Premier League campaign with a trip to Brighton on Sept. 14.