He explained the Scots star played an important but unheralded role in encouraging the chart-topping group to "ham up" their characters, which helped them top the charts around the world, generating millions of pounds.
Mr Fuller points out in a documentary for BBC Radio 2 that Ms Lennox may not be too happy to have her formative role in shaping the band made public.
He said: "I'm not sure this story has ever been told and Annie might not thank me for telling it. But I think we were flying to New York and I sort of brought up midway in the flight and said I've just signed this girl group. And Annie was very interested.
"Almost directly she was the one who got them to be louder and more brash."