Last month, Bowyer replaced outgoing boss Karl Robinson on a caretaker basis, but the former midfielder has won all three of his games in the dugout.
The Addicks are currently up for sale with two parties said to be interested in completing a takeover of the League One outfit, and it has been agreed by both that Bowyer will continue to lead Charlton for the remaining fixtures of the campaign.
Club director Richard Murray said: "Lee has done a fantastic job since taking charge and the results demonstrate the players have really responded to him. You can also hear the relationship he, along with Johnnie [Jackson], have with Charlton fans from the reaction they get on a matchday.
"The takeover hasn't moved as quickly as we had envisaged and it was important for those players and fans to know that whatever happens there will be stability.
"At this stage, there are still two parties looking to purchase the club and everything is close but a date for a takeover is not something I am able to put a timeline on because, as we have seen, these things can take longer than expected."
Charlton currently sit in sixth place in the third-tier standings.