The aircraft carrying Chilima, 51, left the capital Lilongwe at 9.17am on Monday but was unable to land at Mzuzu airport as scheduled at 10.02am due to poor visibility.
It was ordered to return to the capital but went off the radar and aviation authorities could not make contact with it.
"I'm deeply saddened, I'm sorry to inform you all that it has turned out to be a terrible tragedy. The search and rescue team has found the aircraft near a hill ... they have found it completely destroyed with no survivors," Chakwera said on Tuesday.
Chakwera said in an address to the nation that the crash site was in a mountainous part of the Chikangawa Forest.
He said the military was bringing the victims' remains back to the capital.
"Despite the track record of the aircraft and the experience of the crew, something terrible went wrong with that aircraft on its flight back to Lilongwe, sending it crashing down and leaving us all devastated," he said.
Chilima, seen as a potential candidate in the 2025 presidential election, was arrested in 2022 over graft allegations.
However, a Malawi court dropped the charges against him in May 2024 after the director of public prosecutions filed a notice for the case to be discontinued. Chilima has denied wrongdoing.
