Nick Holzherr has secured £170,000 to launch Whisk, service that creates online shopping lists based on recipes.
In the TV series, Lord Sugar told the entrepreneur that he was not convinced the website would be "useful".
Mr Holzherr told the BBC his new investors were "knowledgeable" about tech, and he had a "scalable business".
Mr Holzherr reached the final round of the reality series in which Lord Sugar whittles down a pool of potential business partners before finally investing in the winning idea.
His idea was to create a website which would allow customers to convert recipes automatically into shopping lists within online supermarkets.
Users could either print off these lists and go to their local stores, or buy directly online with "one click". Whisk would take a cut of the online transactions.
Speaking of Mr Holzherr's plan, Lord Sugar said on the show: "It's achievable, I get that. But so's sending a man to the moon. What are we going to get out of it at the end?"
"Who could be bothered with it?"
Mr Holzherr said he had overcomplicated his proposal during the show.
"I explained it too technically, too many details - it meant it wasn't really understood," he told the BBC.
He said since the show he had had significant interest from members of the public, "particularly mums", who were keen to see the project get off the ground.
Also interested were four investors who stumped up the funding which Mr Holzherr said would be spent on hiring new staff and developing the platform.
One of the site's investors, Midlands-based entrepreneur Doug Scott, said: "Quite simply, blending recipes with online shopping is a space in the online world which remains untapped but certainly won't for much longer."
Mr Holzherr said he hoped the site will launch in two to three months time.
"I was trying to stress to Lord Sugar and his advisors that you don't need a lot of money to build this," he added.
"We're hoping we'll be able to generate revenue quite quickly."