The 24-year-old Wanderers midfielder had been receiving treatment at the London Chest Hospital since suffering a cardiac arrest during a match against Tottenham Hotspur last month.
Coyle, who spent several days by Muamba's bedside during the early part of his recovery, has revealed that everybody connected with the club is "delighted".
"It is absolutely fantastic news that Fabrice has been discharged from hospital and everyone at the club is delighted," Coyle told the club's official website.
"We would also like to add our thanks to the staff at the London Chest Hospital for their care and treatment of Fabrice, which has been outstanding.
"It is important that Fabrice and his family are now given time and space to be together, and we would ask the media to continue to respect their privacy."
Muamba joined Wanderers in 2008 from Birmingham City.