Muir has been in talks with Charlton owner Roland Duchatelet about a takeover for months but a deal has still not been struck and Duchatelet has moved to keep Bowyer in charge.
Charlton say “the club’s ownership remain very hopeful of the takeover” but said in a statement that Bowyer will “take up the position until further notice”.
Charlton said: “With no confirmation of the much talked about takeover, the current ownership has been in London this week to make provisional decisions to allow the club to best prepare for the start of the 2018-19 campaign.
“The club’s ownership remain very hopeful of the takeover but felt it could not be left any longer to make key decisions with the season fast approaching and the players due back for pre-season at the end of the month.”
Bowyer did a good job to lead Charlton into the play-offs as caretaker manager at the end of last season and wants the job on a full-time basis.
Bowyer said: “I am looking forward to working with the group again. They put a great shift for me and the club last season and I want to build upon where we left off.”