Totton defeated Luisa Zissman in the show's finale, with Sugar opting to invest in her cosmetic clinics business rather than Zissman's wholesale bakery concept.
Sugar described both finalists' business plans as "credible", but he appeared to be swayed by Totton's final plea in the boardroom.
"I think I'm first of all pitching a fantastic business opportunity, completely unique, and it's extremely lucrative," said the doctor.
"And also, you're investing in me as a person and I genuinely think I'm a dependable, trustworthy person to invest in. And I really think that this is a fantastic opportunity for you and myself."
Explaining his final decision, Sugar said that it was the "devil" in him that made him invest in Totton's "risky" business.
"Leah's a very determined young woman, and it's a very interesting industry, and she's the most interesting candidate, and she has the most interesting business proposition," said Sugar.
Speaking in the famous AMS 1 car after her victory, Totton said: "To have Lord Sugar show this faith in me is absolutely unbelievable, it's amazing. I had much less experience than the other candidates in business coming in to the process and I really can't believe that I have got this far and that I've actually won it! I can't believe it.
"I'm really going to do everything that I can to prove that he has made the right decision and I won't let him down."
Losing finalist Zissman claimed that she was happy to come second to an "amazing girl" like Leah. "We are very close and I'm so happy for her," she said.