The Edinburgh businesswoman, who reportedly made £40million from the sale of her IT firm in 2005, will take control at Hearts when a deal to take the club out of administration is completed after putting up the £2.5million needed to satisfy creditors.
Fans will ultimately assume control through the Foundation of Hearts but their initial fundraising will provide working capital before money is used to pay back Budge and transfer ownership.
In an email to supporters, the "executive chairwoman designate" said: "We all know the task ahead. Firstly, to ensure the club survives; secondly to ensure it is re-stabilised financially, with the strongest possible foundations to ensure its future. These are the tasks I am offering to take on; but I will not succeed without your continued support.
"My task, as I see it, is to ensure that when I hand the club over to you, the supporters, I will be handing over a club in good shape and with sufficient resources to face the challenges of the future. To achieve this the club needs investment over the next two years to stabilise and then build a solid financial base.
"Some of you are asking how long you might be asked to contribute. Right now, the club needs your financial support to see us through the next two years. Thereafter your contributions are required to secure supporter ownership.
"Beyond that, and once ownership passes to the fans, it will be for you, the supporters, to agree the financial priorities of your club.
"To all the supporters who are helping the club, either by attending games, contributing to the Foundation of Hearts, buying merchandise, fund raising - the list goes on - I thank you.
"It has been said many times over the last few months, but it is absolutely true that without this support we would not be here today.
"To those of you who have already pledged, I thank you.
"To those of you who have not yet done so, I would simply say that if you believe in the journey we are about to undertake, and only if your financial position allows it, please consider joining your nearly 8000 fellow supporters, who are contributing.
"These supporters have started to build the cash reserves to enable fans ownership to become a reality, which will ultimately put an end to private ownership of our club.
"I will do my part to the best of my ability."
Fans will initially provide £1million to help stabilise the Scottish Premiership's bottom club when they come out of administration. That is not expected to happen before the end of March as legal agreements with major shareholders and creditors UBIG and Ukios Bankas need to be ratified in the Lithuanian courts.
Supporters, who will be represented on a new board from the start, will then provide at least £2.8million in working capital over the next two seasons before repaying Budge her £2.5million outlay.