Dewberry, 26, from Hull, wins a six-figure salary job at Sir Alan's Xenon Green division, a business that uses environmentally friendly methods to dispose of used computer equipment.
Her cool and calm demeanour, which earned her the nickname "The Silent Assassin", held off competition from more than 10,000 entrants -- the largest amount the show has attracted.
The 12-week series, a hit for BBC Two, regularly attracted more than 4m viewers and had contestants battle against each other to impress Sugar to win a job at his company.
Weekly challenges included working on the sales floor at Top Shop, leasing flats and designing a charity calendar for Great Ormond Street Hospital.
Last night's episode had Dewberry managing a team of the series' fired apprentices at a lavish James Bond-esque casino party at London's Tower Bridge. Previously, she had won seven rounds to make her way to the final.
Dewberry said: "I've worked incredibly hard over the last few years to build a successful career and have Sir Alan as a mentor will complement that further.
"For someone like Sir Alan to recognise my ability is unbelievable. It wasn't until right at the very end when he said I'd won that I believed it."
Sugar said: "All [Michelle] has done in her life is work hard and she has become a great achiever.
"I found her very focused, very determined, very organised, and this particular job I have in mind requires all of those skills."
Sugar said to runner-up Badger: "I was really stuck this time, no one can dispute your skills, you are a great success and I'm sure we'll meet again in the future."
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