Former Labour MP Dawson was suspended from his role as chief executive in September last year, after allegations relating to his conduct were made.
Following an independent investigation and subsequent mediation, BASW said that Dawson will not return to the organisation, and that a mutual agreement on the issue has been made.
Current acting chief executive Bridget Robb will remain in charge while a decision on a permanent replacement is taken. Details of the allegations against Dawson have not been made public.
Fran Fuller, BASW chair, said: “I would like to thank Hilton for his contribution to BASW over the past three and a half years, which have been some of the most successful in the history of the association.
“Despite the difficulties of the past few months, I am pleased that this issue has now been resolved, allowing everyone to move on. I wish Hilton the very best in the future.”
The investigation into the allegations was completed in December.
Dawson said: “I thoroughly enjoyed my time as chief executive and believe that I leave the association in a stronger position than ever to move forward and continue to represent the interests of social workers as no other organisation can.
“The past few months have not been easy but I am pleased to be able to leave BASW on good terms and move on to a host of new opportunities.”
Dawson began his social work career in Northumberland in 1979. He was elected Labour MP for Lancaster and Wyre in 1997, standing down in 2005.
After he left politics, he was a project manager at ChildLine, then chief executive of the charity Shaftesbury Young People and chair of the National Academy for Parenting Practitioners, before taking up the post at BASW.