Despite no win in eight since taking over, and a club record no win in 16, the board have put faith in the former Hull and Colchester manager and have said they expect four new faces to arrive in the January transfer window.
Chairman Richard Murray said, "With 20 matches remaining this season, we were aware that time was an issue, particularly with the January transfer window opening on Thursday,"
"Phil knows the players, knows the strengths and weaknesses of the side, and has huge Football League experience. Perhaps most importantly, he is a strong character, and knows how to battle against adversity."
"There has been a lot of hard work behind the scenes and performances have improved, although that hasn't been shown by results yet," said Murray.
"We've looked at the alternatives, but the calls and discussions we've had, given the current situation, have led us to conclude that there is no one better than Phil to turn things around, and we believe any money the club currently has to invest must be spent on the pitch.
"Changing managers and the backroom staff comes at a very high cost, and it's clear we need to focus any investment on the pitch because that is what will really influence matters entering a hugely important period for the club.
"We need someone who can operate smartly during the January window and someone in place for the biggest game of the season, our next league match against Nottingham Forest on January 10th when it's absolutely vital to pick up three points."
He added: "I've been greatly impressed by Phil's motivational skills, and with Mark Kinsella and Phil Chapple, both of whom have Charlton running through their veins, supporting him, we feel they are capable of doing the job that is required.
"The board will also provide as much support as possible, and it's clear that we need to look at bringing a number of players, maybe three or four, to the club as soon as possible."
Parkinson's first game in charge is Saturday's FA Cup Third Round match against Norwich at The Valley.