He replaces Barry Smith who was sacked earlier this week, with the Dark Blues sitting 15 points adrift at the base of the table.
A statement on the club's website reads: "Having been inundated by high calibre candidates over the last few days, one man stood out as perfect for the position of interim manager of Dundee FC.
"John Brown is a man with real heritage and history at Dundee FC and when at Dens Park in his time as a player, he was a real inspiration, a fans' favourite and scored some vital goals and he has never lost his feelings for the club."
As a player with Rangers he won six league titles, and was also a member of the coaching staff at Ibrox.
Although relegation looks a near certainty, Dundee have a huge match a week tomorrow when they face city rivals United in the William Hill Scottish Cup quarter-finals.
The club statement continued: "Having met and spoken with members of the board and CEO Scot Gardiner this week, his passion for Dundee was instantly evident and his willingness to step up to the plate for the remainder of the season alongside his immediate understanding of what we as a club need from the position, convinced us he is the man to address the challenges ahead of us.
"There is still a lot to play for this season with some vital games coming up and John will make sure that the Dundee fans see and understand that he is here to make a difference and he is looking forward to working with assistant manager Ray Farningham, the coaching staff and our full squad of players.
"The club will continue to assess and review the longer term situation but as we have highlighted, due to the mixed challenges of our current league position and the uncertainties over league reconstruction, it is impossible for us to set a budget for next season and coming years.
"Hopefully that position will become clearer very soon and we will then look to appoint a manager in a full time, longer term position.
"In the meantime we hope that every Dundee fan will rally behind John and the team for the remainder of what can still be an exciting and historic season."