The group had distinct personalities when they burst onto the music scene in the late Nineties, and were eventually branded Scary, Baby, Ginger, Posh and Sporty – nicknames that still exist today.
Fuller told BBC Radio 2 that Lennox may not be too happy to have her formative role in shaping the band made public.
He said: “Each of the girls knew who they were and in their own way tried to represent it but it wasn't strong enough and probably the most significant thing that happened was when they met Annie Lennox.
“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.
"She said 'I want to meet them'. Almost directly she was the one who who got them to be louder and more brash and more specific, So Emma who was the sweet cute blonde girl becamse Baby Spice. She just played it and hammed it up - none of these names actually existed, but Annie gave them focus."
In the programme, The Fuller Picture: The Simon Fuller Story, he also tells how his "controlling" influence on the girls led to him famously being dumped as their manager when they were at their peak in late 1997.
He said: “I was the sergeant major, I was the parent, I ran everything. I was very controlling and I think that builds up some resentment. They were probably unhappy because they were missing their parents, missing their loved ones, they were tired, emotionally drained and I was probably the one responsible for that so we parted company.”
He added: “It was kind of somewhat out of the blue. My initial reaction was kind of shock, and, fine, OK, that's that. Sod them, I'm moving on. They're missing out on having the best manager in the world and that's the way it is, so I withdrew and stopped managing them instantly.”
He revealed he already had plans for a second Spice Girls film and third album before he was fired by the girl band.
"It would have set each of them up with solo careers beautifully. It wasn't to be. I completely understand how it happened."
The Fuller Picture: The Simon Fuller Story is to be broadcast by Radio 2 tonight at 10pm