Bowen, 58, worked alongside Mark Hughes with Wales, Manchester City, Blackburn, Fulham, QPR, Stoke and Southampton.
The former Wales international managed Reading in the 2019/20 season – guiding them from 23rd position in the Championship to 14th.
He replaces Mark Robinson who was sacked as head coach on Monday and his first game in charge is at Sheffield Wednesday on Saturday.
“I am deeply honoured to have been offered this position,” said Bowen.
“I fully understand what’s at stake and what needs to be done over the remaining seven games. Take my word for it, we will all be doing everything possible to keep this proud club in League One.”
Bowen will be assisted by former Arsenal and Chelsea coach Eddie Niedzwiecki, who also worked with him at Reading.
Mick Buckley, the Dons’ interim chair, said: “We are excited to be welcoming such experienced and respected coaches at this stage in the season.
“Mark understands the enormity of the job ahead. In many respects it speaks volumes for his character and personality that he is willing to take on this challenge with so much at stake.
“We can only do everything we possibly can to support him to the hilt and I’m confident that’s exactly what our fans will be doing on Saturday and for our forthcoming home game against Charlton on Tuesday.”