The 19-year-old beat Emma Grattidge to the title after they went head-to-head on a catwalk for designer Pavoni.
Anita Kaushik finished in third place following a 'tribal Goddess' photo shoot on a Canadian beach, which required the girls to pose with a horse.
As part of her prize, Letitia landed a contract with international agency Models 1, a cover and fashion shoot with Company and a contract with Revlon.
She will also front an international campaign with Miss Selfridge, enjoy a holiday to Dubai and live in a luxury apartment in London.
Speaking to Digital Spy after her victory, Letitia declared: "I still can't believe I've won. It literally feels amazing. I feel like I'm on top of the world right now.
"I just feel in my gut that this is something that is going to completely [start] a whole new time in my life."
Although she felt like she had "a lot to prove" coming into the final, Letitia said she was pleased to see judges Elle Macpherson and Tyson Beckford fighting her corner.
"Elle really, really [was] passionately... rooting for me to win. And Tyson as well," she noted.
"It really makes me think that I can do well in the industry because they've been doing it for so long and I know that Tyson has helped so many models to get successful, so obviously they know what they're talking about. If I was crowned the winner with them as judges it does give me hope for my future really."
She continued: "They've seen something special in me that they really seem to like - it's [me] walking in the room and standing out and that fire in my belly, the way [I] strive to do really well."
Letitia said that she had received "very positive" comments from Revlon and Company while working with them and added that she dreams of appearing on the cover of Vogue and fronting a Victoria's Secret campaign.
Declaring that Next Top Model had "matured" her, the 19-year-old finished: "I really am working hard.
"I'm working out and trying to learn as much as I can as quickly as I can, because I've obviously got lots of models with years of experience against me. I want to not just be a model, but a supermodel."