Knox and Brown will be up against their former team on Saturday
Motherwell have withdrawn their complaint against Aberdeen over the departure of Craig Brown from Fir Park.
Brown and his assistant Archie Knox resigned from their posts to join the Dons last week.
The pair were working without contracts but the Lanarkshire club felt Scottish Premier League rules had been breached.
However, they have now informed the SPL that their grievance has ended following "constructive discussions" with the Pittodrie club.
"During a difficult time for Scottish football and when clubs are about to enter discussions on a major league restructuring, we are of the view that it is not in anyone's best interests for two Scottish Premier League clubs to be involved in an ongoing dispute," read a statement from Fir Park.
"Following constructive discussions with Aberdeen, we have reached an agreement to draw a line under the matter and have formally withdrawn our complaint to the SPL in relation to their employment of Craig Brown and Archie Knox.
"We have always maintained a good working relationship with Aberdeen and look forward to that continuing in future.
"We strongly believe this action is in the best interests of the club and will make no further comment on the matter. We will now focus all our resources on employing a new management team to take the club forward."
Dons chairman Stewart Milne had earlier refuted claims his club acted inappropriately.
And, commenting on the resolution, chief executive Duncan Fraser said: "As I stated at the start of the week Aberdeen and Motherwell have always enjoyed an excellent relationship.
"At no point was the integrity of Craig or Archie questioned by either club and we believe that we acted accordingly throughout.
"Both Aberdeen and Motherwell have played significant roles working with others on the challenges facing Scottish football and want to draw a line under the events of the last few days."
Brown stepped down as Motherwell manager last Thursday and was unveiled as the new Aberdeen boss on Friday.
The veteran pair have both agreed two-and-a-half year deals to take over the helm at Pittodrie and will be up against their former team on Saturday.
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