McCann left the club three days ago having guided them to Premiership safety in a five-week spell in charge.
The 42-year-old had indicated he was going back to his previous role as a television pundit.
"I have had time to think about the opportunity of being manager of Dundee FC full-time and decided it was too good for me to turn down," he said.
"I'm looking forward to being in charge for the new season and work has already begun on a number of fronts. I'm excited about the future and can't wait to get started."
McCann took over from the sacked Paul Hartley on 18 April with the club sitting in the relegation play-off spot.
However, the former Dark Blues winger won his first two games as interim manager and drew a third, before rounding off the league campaign with two defeats.
Dundee managing director John Nelms said the club had been "inundated with applications" for the role and that, after discussions "with a number of candidates", McCann had been the club's "number one choice".
Following McCann's initial decision to step down, St Mirren rejected a request by the Taysiders to speak to their manager Jack Ross.
Interim boss Neil McCann has reversed his decision to leave Dundee and taken on the position long-term.