The 20-year-old midfielder becomes Megson's first signing of the summer after he agreed a four-year contract at the Reebok Stadium.
Megson said: "Fabrice is a tough-tackling central midfielder who has had a good grounding with the Arsenal youth set-up.
Muamba came up through the Arsenal youth system before initially joining Birmingham on a season-long loan deal from the north London outfit at the beginning of the 2006-07 season.
He made 34 appearances for the Blues before making his stay at St Andrews permanent and netted two goals for the West Midlands club in 37 outings.
Born in the Democratic Republic of Congo, Muamba moved to the UK in 1994 and became a naturalised British citizen.
He subsequently made his England Under-21 debut in the friendly match against Romania in August 2007 and has since gone on to make a further six appearances at that level.