The swimwear fashion brand owner from Leeds, 26, was handed a £250,000 investment by the business tycoon.
Gabbidon was crowned winner after the final episode of series 14 saw her and runner-up Camilla Ainsworth present their business plans to more than 200 experts at London's City Hall.
Speaking to the Press Association, she said: "I've been speechless since I've known. I can't believe it's happened. Not that I didn't think I could win it but it's just real. It's crazy. I'm absolutely over the moon."
Gabbidon added: "We went in guns blazing, both of us, we both said things about each other's businesses, but at the end of the day I did come in this to win. I'm sure Camilla will be massively successful in whatever she does.
"For me, I wouldn't have entered the show if I didn't think I had it in me to win. I would say that it is very easy to underestimate how hard the tasks are. I'll never, ever judge any of the other candidates. It's so hard to put yourself through the tasks.
"(Working with Lord Sugar) is the biggest challenge I have ever had in my life. There's no way I'm going to let the biggest challenge take me out. I am nervous but I'm ready."
Ainsworth, 22, said: "Although I would have loved to win, I'm just really proud of myself as the youngest ever finalist of The Apprentice.
"It takes a while to sink in but immediately I was kind of in fight mode. As a person I am very positive and optimistic. I gave myself a good few seconds to be quite gutted then I thought, 'Right, reset and go again'."
She said: "It's £250,000, it's not pocket change. You've got to be out there for yourself. As much as me and Sian are bezzies, we both are massive, massive lovers of success and we both wanted to strive for that prize."
In the final episode, the pair welcomed back the contestants Lord Sugar had previously fired, to help them create a video advert and billboard for their companies.
They then had to give a pitch to a group of industry experts, who shared their thoughts on the business plans with Lord Sugar.
Ainsworth said appearing in front of the panel, which included leading business people from the fashion and health drink worlds, had been a frightening experience.
She said: "I was absolutely petrified. I had my Britney microphone on and I was trying to psych myself up. For one moment I did have the flight or fight. I thought, 'I could do a runner now'.
"I did feel the pressure in that last task, I won't lie. I haven't had any direct experience pitching to that many people, not since I was in nativity at school."
After a final impassioned pitch from both candidates, Lord Sugar made his decision.
He told them: "Camilla, I've said to you earlier on, I find you a big risk, a very, very big risk. Having said that, there is a growing market here.
"Sian, it's a crowded market - that's a big, big concern for me, but you are an expert in your field, and you are a good designer, there's no question of that.
"I think that yours is a growing market (Camilla), and yours is a massive market (Sian), it's very tough for me to make a decision. But on reflection, Sian, you have a great aptitude and a talent for design - you're going to be my business partner."