The charity called the review in December.
Grey London was the incumbent on the creative business and MediaCom previously handled the media account.
The agencies have been tasked with creating a "bigger, braver and bolder" new look for its "end the awkward" campaign which aims to change attitudes to disability.
Lisa Quinlan-Rahman, the director of external affairs at Scope, said: "We’re impressed by George & Dragon’s approach and how well it tested with our core audiences and disabled people.
"Scope has a talented, in-house creative team and we’re looking forward to working collaboratively with our agency partners for this next, exciting stage of 'end the awkward'."