Members of the public donated the entire sum needed by Manjit's Kitchen to open a new restaurant with later opening hours than their present stall in Kirkgate Market.
Owner Manjit Kaur and her team specialise in cooking vegetarian Indian street food, and the business has won a BBC Food and Farming award.
Manjit, from Chapeltown, decided to launch the Kickstarter campaign rather than apply for bank loans to fund her new venture.
Anyone who supported the project will receive rewards such as free meals and cookery classes in return for their pledge.
The campaign ran for the month of October, on the proviso that backers would have their money refunded if the target was not met. The Â£40,000 figure was exceeded a week before the deadline.
Manjit has already raised a third of the projected opening costs herself and is currently looking at potential premises in the city centre.
She has run her stall in the market's food hall since 2016, and before then had a converted horsebox which she would take to weddings and festivals.
"We have learned lots running the cafe and are now ready to take this learning forward and open another place," said Manjit.
"As we are based in the market, the cafe closes at 5pm. We have therefore built the cafe on lunchtime trade only. We now want to build another place we can open in the evenings too.
"I want to employ more people and continue to develop our style of Indian vegetarian food. We can develop our drinks offer by expanding our partnerships with local breweries and creating a cocktail menu.
"I believe a thriving, independent business scene is important to a city and we want to be part of that. We work closely with local charities and through our business we want to make Leeds a better place."
The cash raised by the Kickstarter funding campaign will be used to purchase kitchen equipment and fit out a new site, as well as for leasing, surveying, legal and licensing fees.
Manjit was invited last summer to serve Indian street food at Manchester City's end-of-season party after winning the Premiership title, and she met stars such as Nicolas Otamendi.