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The Addicks dispensed with the 39-year-old former midfielder despite a strong start to his time in the dugout at The Valley, but he is back in management across the capital with the Dons.
“I cannot wait to get started,” Jackson told the club website on Monday.
“I am extremely familiar with the AFC Wimbledon story and have total respect for what the fans have achieved - especially the marvellous new ground.
“AFC Wimbledon and The Cherry Red Records Stadium don't belong in League Two and I'll be doing everything possible to get us back up again.”
Terry Skiverton will assist Jackson at Wimbledon as the club looks to bounce back to League One, after they were relegated under Mark Bowen having failed to win a game since December 7.
Club interim chair Mick Buckley added: “We are thrilled to be making these appointments. Johnnie had a successful first season as manager at Charlton last season following four years in assistant/caretaker manager roles.
“We wanted a young, hungry manager with a point to prove and that, coupled with his demonstrable knowledge of how to get results, gave him the edge over a strong field of candidates.”
Shortly after Jackson’s announcement at Wimbledon, predecessor Bowen was confirmed as the new head of football at Reading, who have made interim Paul Ince their permanent manager ahead of the new Championship campaign.