The 61-year-old had been chosen by the Spanish club's administrators as their new owner in May, with the next step being to negotiate the repayment the debt of 320 million euros with Spanish bank Bankia, who had lent the amount to Valencia.
A statement on Bankia's website was released on Friday confirming the bank had agreed terms with Lim's Meriton Holdings company to restructure the debt, adding that the offer was "executable, consistent and credible".
"The transaction is structured so that it would allow Bankia the possibility of fully recovering all funds granted in the past to both the Club and its Foundation VCF, for a total amount of circa 320 million euros," part of it read.
"The terms are subject to meeting certain milestones and final legal documentation to be agreed by both parties."
Lim, who has a reported value of £1.4 billion according to Forbes magazine, will reportedly have a 70.4% stake in Valencia and he told the club's website that their supporters "can finally be finished with months of uncertainty".
A Meriton spokesman described the company as being "glad" to have struck a deal with Bankia, according to Channel News Asia.
"This is indeed a significant milestone - this agreement will set us on a path to provide the club with long-term financial stability on a sustainable basis," he said.
"We will be able to implement our strategic plan and the club will soon be able to compete at the highest levels of European competition.
"The [acquisition] process remains a complex one but we are confident that we will be able to finalise the in-depth legal details with the cooperation of all parties involved."