Sunderland have been looking for a new manager since opting to sack Phil Parkinson and were flooded with applications for the post at the Stadium of Light.
They have turned to former Bristol City boss Johnson and held face to face talks with him, selling the job at the club to the 39-year-old, who has been out of work since being sacked by the Robins earlier this year.
It is claimed that Johnson has now given Sunderland the green light and told them he is willing to take the job.
The paperwork relating to the move is now being completed and Johnson is expected to then be announced as the new Sunderland manager.
He will take over a side sitting in seventh spot in the League One standings and hungry to win promotion back to the Championship this season.
Johnson experienced promotion from League One as a player with Bristol City in the 2006/07 season and will look to repeat the trick as a manager.
He spent over four years in the dugout at Bristol City and prior to taking over at Ashton Gate enjoyed spells in charge of Barnsley and Oldham Athletic.