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.
"He's played in the Premier League with Birmingham City and he'll be a tremendous asset to Bolton Wanderers over the coming seasons."
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.