The fate of the 140-year old institution has hung in the balance ever since it was plunged into chaos on June 19 last year with more than £25million of debts; a 15-point deduction for the start of this season's SPFL Premiership campaign making matters worse.
However, a deal was struck on Wednesday with Ukio Bankas - the club's largest creditor - for Budge and her BIDCO 1874 company to buy their 29.5% share in Hearts, following a previous agreement last week to take a 50% holding from UBIG, the fallen bank's parent company.
Due to the protracted nature of matters so far, along with complex stock market regulations relating to the purchase of shares, doubt remains over how long it will take for matters to be concluded, with concern over Hearts still not having exited administration by the time next season starts, thus leading to a potential points penalty in the SPFL Championship.
However, Budge yesterday looked to allay fears with the 66-year-old, who was at Tynecastle to watch Hearts' 2-0 win over Ross County, stating her £2.5m takeover should be completed before next season gets under way on August 9.
"The last stage, in terms of the dealings with the current owners, is to complete the legal Sale and Purchase Agreement (SPA),' said Budge. "We are all working very hard to get the final negotiations completed and the associated legal processes finalised. We are all very confident that this work will be completed well before the start of next season."
Budge's plans for who will look after footballing matters remains unclear, however. In her statement, she makes reference to meeting with the 'current' management team to implement her plans over the summer, raising questions about Gary Locke's long-term future.
But speaking after yesterday's match Locke insisted he was content to wait for his fate to be decided.
"I can only keep doing my job and the more games we win the better it is for everyone," he said. "I know Ann is working tirelessly behind the scenes. So when she gets round to discussing things with myself I'll look forward to that.
"It would be fantastic [to start next season out of administration], you have seen how costly it has been this season. It's been a really positive week for everyone connected with the club."