Royal Bank of Scotland is putting up £2.5 million with The Hunter Foundation pledging £700,000 to carry the competition through to 2017.
Those sums will be added to the Scottish Government's existing £2.35m pledge. An as yet unnamed new charity, which will be a subsidiary of The Hunter Foundation and have an independent board of trustees, will be set up to manage the £5.55m pot.
Alongside that, the Edge fund will convert from giving out solely grants into awarding a combination of loans and grants.
Sir Tom said that will help the Edge move towards a sustainable model where the loan repayments can be used to fund future awards.
He said: "We are not tying people up in loan agreements. We are saying if the business doesn't work out then that is a shame and nobody is going to chase you for the money.
"But if it does work out then pay us half back as that will fund the next entrepreneur in line.
"It is an honour system that we have seen working with Muhammad Yunus at Grameen Bank, and were very impressed with that."
Along with the funding the Edge applicants will receive a range of business mentoring while the likes of Business Gateway, Scottish Enterprise and Highlands and Islands Enterprise will continue to be involved.
Sir Tom suggested he was hoping to open the door to a broad range of contributors including Entrepreneurial Exchange and the Saltire Foundation.
He said: "In all my experience of doing this it is never just about the money. The mentor[ing] and the help from someone who has been there and done it is as important, if not more important, than the cash. There is a rich seam of mentors to tap. What I am trying to do is not reinvent the wheel, but bring everybody into the tent. Scotland has got a good community and successful people want to give something back."
Even those who apply to the fund and are not successful are to be offered training and mentoring opportunities.
Sir Tom said: "There is nothing more disheartening than applying for something and getting turned down. 'Not yet' might be the answer to some of the people but then [we can say] here's where we think you went wrong and here's how we can help to get it right."
Sir Tom said he was backing the fund for the long term and would consider funding it beyond 2017 if necessary. He said: "There is no point in funding low quality businesses, we have to help them get up the curve and be better. [The funding] is totally dependent on the quality of businesses that come forward."
A chairman of the charity is expected to be appointed imminently, although Sir Tom ruled himself out of taking that position.
To date, 69 businesses have shared £2.56m of funding since the Edge fund was established in 2012.
The first 54 winners are said to have created more than 120 new jobs, generated an additional £5m of turnover and raised £3.5m of investment. Assessment of the most recent 15 recipients has not yet taken place.