Mr Slater's resignation was first tendered prior to the monthly meeting of club representatives on August 26.
He had a change of heart but, at last night's September meeting of the management committee in Burnley, it was decided that it should be accepted by the reps.
It is understood that there was at least one abstention but that no-one voted against it.
The league issued a short statement thanking Mr Slater for his services as assistant secretary and secretary over the past seven years.
They have also asked assistant secretary Lionel Cooke to stand in until the AGM when he will be nominated for the post of secretary.