The move will provide financial relief to the country, which in 2020 became the first in Africa to default after the Covid pandemic.
"The Ministry of Finance... is pleased to announce that a Memorandum of Understanding (MoU) has been agreed with its Official Creditor Committee (OCC) on the comprehensive debt treatment," the ministry said.
"Each official creditor will now begin their internal process to sign the MoU."
Zambia had reached an agreement in principle with its creditors, which include China and Western nations, on $6.3 billion of its debt in June, but the deal had yet to be finalised.
Earlier this week, the International Monetary Fund said the deal was expected to be signed soon, after the institution's chief prematurely announced it had been signed.
"The next step is to secure a comparable agreement with our private creditors," Zambian Finance Minister Situmbeko Musokotwane said.
"Our government committed to resolve the mounting debt suffocating our economy and we are proud of the immense progress we have made. Once completed, debt restructuring will free up resources vital for this government to invest in our development agenda."
Concerns over debt in low-income nations have been at the forefront of talks of the IMF-World Bank meetings in Marrakesh, the first to be held in Africa since 1973.
- Servicing struggles -
Central banks worldwide have raised interest rates in efforts to tame inflation, which rose after Covid restrictions were lifted and jumped higher after Russia invaded Ukraine.
Zambia, whose total debt amounted to $32.8 billion at the end of 2022, defaulted on its $18.6 billion foreign debt in 2020 at the height of the Covid-19 pandemic.
Musokotwane said this week that 90 percent of his country's budget was going towards paying public servants and servicing the debt.
The managing director of the IMF, Kristalina Georgieva, said from day one that holding the IMF-World Bank meetings in Africa was "symbolically and substantively very important."
"A prosperous world economy in the 21st century requires a prosperous Africa," she said.
More than 20 African nations are either already in, or on the edge of, debt distress.
In some, more than 40 percent of the state budget goes to servicing the debt -- an unsustainable level in countries that need to maintain basic public services such as water and electricity.
But negotiations to restructure debts have become more complicated over the years as new creditors such as China, Saudi Arabia and Brazil have emerged, in addition to private lenders.
Now countries must negotiate terms with China and the Paris Club of creditors, which mostly comprises Western nations with very different policies to Beijing.
Zambian President Hakainde Hichilema visited China, the country's main creditor, last month.