The 25-year-old received a £250,000 investment for her cosmetic procedures business after the guru told her "you're hired" in Wednesday's final.
Totton, who becomes Lord Sugar’s new business partner, pipped to the post Luisa Zissman, who had pitched an online wholesale baking supplies business.
Miss Totton plans to offer anti-ageing skin treatments at a chain of clinics across the UK.
Previously called NIKS Medical, the name has changed to Dr Leah at Lord Sugar's request.
The Londonderry doctor is continuing with a masters degree, and plans to keep up her clinical skills by working as a locum.
Totton hopes to raise the standards of the beauty industry with her medical credentials.
"To have Lord Sugar show his faith in me is absolutely unbelievable. It's amazing,” she said.
"I had much less experience than the other candidates in business coming into the process and I really can't believe that I've got this far and that I've actually won it."
The finalists brought back previous candidates to help them in branding and marketing their business plans, before presenting them to industry experts.
Luisa broke down in tears after feeling she'd ruined part of her pitch. She floundered on a question regarding her expected profit in five years’ time.
Dr Totton managed to convince Lord Sugar about the ethics of her firm. "I want to ensure these treatments are carried out in a medical environment by properly trained medical professionals.
"I’m a woman and I'm interested in appearance. It worried me to see these procedures done by people who are not medically trained.
"We need to be clear I’m not going into this to encourage women to have these treatments, the market is already there."
Speaking after the final, Lord Sugar said: "We had two great candidates in the last two, but I think that in the case of Luisa she has three businesses already.
"This is an interesting industry in which business margins are very good and she was the most interesting candidate as far as I was concerned."