Robinson left the club yesterday by ‘mutual respect’ with the club in the midst of a 21-game run without a win in all competitions.
Charles, 34, helped AFC Wimbledon win promotion from League Two in 2016 and returned to the club in July to provide defensive cover following a successful spell at Wycombe Wanderers.
The Dons lie fourth bottom in the League One table, three points better off than Doncaster Rovers.
They travel to Sheffield Wednesday on Saturday.
Charles said: “I have seen first-hand the fight and spirit within this squad. There are still 21 points to play for and nobody will be throwing in the towel.
“Of course, none of us want to be in this position but we have a job to do and we will give it everything we have - not just for the club and the fans but also for Robbo, who instilled so much belief in these players.”
Mick Buckley, AFC Wimbledon’s interim chair, said: “Darius has a big, positive personality, great playing experience and we are extremely grateful that he has agreed to take on this role.
"It is our intention to bring in an experienced manager to work with the team for the rest of the season. We are in discussion with some already and we will bring you more news as soon as we possibly can.
“In the meantime, I can only urge all our fans to get behind Darius, his staff and the players. We have been in this position before and history proves that when AFC Wimbledon is truly united in the ‘run in’ then anything is possible.”
Former Newcastle United manager Alan Pardew is the current favourite for the vacancy with the bookmakers.
Portsmouth’s Danny Cowley also features in the betting, alongside ex-Rovers manager Darren Ferguson.
Ex-Blackpool, Crystal Palace and Leicester City boss Ian Holloway is in the frame too, according to the bookmakers.
AFC Wimbledon next manager odds
Alan Pardew – 4/1
Darren Ferguson – 7/1
Neil Harris – 9/1
Luke Garrard – 9/1
Ian Holloway – 12/1
Alex Revell – 12/1
Danny Cowley – 16/1
(Odds courtesy of bookmakers Paddy Power)