Vitoria Mario, who is Portuguese but has lived in the UK for four years, said she was ineligible for Government funding and her family could not afford to support her while she studied at the University of Warwick.
She told the PA news agency she has not yet spoken to the singer but would like to thank her.
“She actually made my dream come true,” Ms Mario added.
Swift’s donation came “out of the blue”, she said.
“I feel like at some points I was worrying too much about the money, what I have to do, if I have to look for a job and now I can just do more maths, prepare myself for uni so I can just be really prepared when it comes,” Ms Mario added.
She said she is surprised the singer came across her campaign given that she is not from the UK.
The US pop star made the contribution via a Go Fund Me page raising money which states that Ms Mario may not be able to take up her university place.
Taylor Swift does it again! 👏👏👏
She just donated exactly £23,373 to put this university student exactly at her fundraising goal: https://t.co/u3eQexFYzC pic.twitter.com/GutunJXAkW— GoFundMe (@gofundme) August 20, 2020
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Alongside the donation for £23,373, Swift wrote: “Vitoria, I came across your story online and am so inspired by your drive and dedication to turning your dreams into reality.
“I want to gift you the rest of your goal amount. Good luck with everything you do! Love, Taylor.”
Ms Mario said her family cannot afford to support her and she needs funds to help pay for her accommodation, a laptop, textbooks and general living costs.
She estimated she would need £24,000 for accommodation, £3,000 for equipment and £13,000 for general living costs including food, transport, gas and electricity.
“Though my story is not unique, my dream of becoming a mathematician is not only a chance at social mobility for my family and I, but to inspire people who have been in similar positions to aspire to be the best version of themselves and strive for their dreams despite gender/racial inequality, immigration issues and financial barriers,” the 18-year-old wrote on her fundraising page.
She added that she has always been “studious” and was unable to speak English when she moved to the UK in 2016.
She was awarded two A*s and an A in her A-levels.
Ms Mario, who lives in Tottenham, north London, said her father has died and her mother lives in Portugal.
Her fundraising page said: “Moving away from her was a challenge but it was a sacrifice worth being made in my family’s eyes.”
Ms Mario, who lives with members of her family, has now reached her fundraising target following Swift’s donation.
