Bohnox Enterprise beat three other bidders for the 14-passenger aircraft used by president Bingu wa Mutharika, who died last year.
"We have accepted their offer and we are waiting to hear from them," Cabinet clerk Ernest Katchetche said in a statement on Tuesday.
The 15-year-old Dassault Falcon 900-EX had been described as being in "perfect flying condition".
Mutharika's successor, President Joyce Banda, decided to sell the aircraft and a fleet of luxury cars used by the big-spending leader.
The government initially set the price at $20-million.
Mutharika controversially acquired the jet for $22-million in 2009, calling it "an asset" for his impoverished country.
Maintainance and insurance for the aircraft reportedly cost the state $300 000 a year.
The southern African nation relies on donor funding to finance its development budget, with half of its 13-million citizens living below the poverty line.
Britain, which is Malawi's main bilateral donor, criticised the purchase of the jet and reduced its aid budget by £3-million.
Since taking office, Banda has introduced a host of cost-cutting measures and uses commercial airlines to travel outside the country. – Sapa-AFP