The plane, carrying Chilima, who was seen as a potential candidate in next year's presidential election, went missing on Monday.
"I’m deeply saddened to inform you that it has turned out to be a terrible tragedy. The search and rescue team found the aircraft near a hill, completely destroyed with no survivors," Chakwera said in a national address.
The aircraft left Lilongwe at 09:17 a.m. (0717 GMT) on Monday but couldn't land at Mzuzu airport as scheduled at 10:02 a.m. due to poor visibility. It was ordered back to Lilongwe but went off radar, and aviation authorities lost contact.
Chakwera confirmed that all passengers died on impact, and the military is bringing their remains back to the capital.
"Despite the aircraft's track record and the crew's experience, something terrible went wrong, sending it crashing and leaving us all devastated," he said.
Images online showed security and rescue personnel at the crash site on a hillside with debris around the tail of the Dornier 228-202K military transport plane, its tail number MAF T03 still visible. Reuters could not authenticate the pictures.
Chilima, 51, had returned from South Korea on Sunday after attending the Korea-Africa summit and was traveling with others to attend the funeral of Malawi's former justice minister.
"Dr. Saulos Klaus Chilima was a good man, a devoted father and husband, a patriotic citizen who served his country with distinction, and a formidable vice president," Chakwera said.
Chilima, former director of Airtel Malawi, led the United Transformation Movement party and partnered with Chakwera to form the ruling Tonse Alliance, winning the 2020 election. However, their relationship had become tense ahead of the 2025 presidential election, where Chilima was expected to challenge Chakwera.
Chilima was arrested in 2022 on graft allegations, but a court dropped the charges last month after the director of public prosecutions filed a notice to discontinue the case. Chilima denied any wrongdoing.
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