Hydara, a critic of Jammeh’s government and co-owner of the independent newspaper The Point, was killed on the outskirts of the West African country’s capital Banjul.
Jammeh fled to Equatorial Guinea in 2017 after losing a presidential election, bringing an end to 22 years in power marked by extra-judicial killings, torture and forced disappearances as well as the pilfering of state assets.
He has not been reachable for comment since leaving the Gambia, but supporters in his homeland have dismissed investigations of him as a witch hunt.
Lieutenant Malick Jatta, the army officer said he was a member of Jammeh’s elite guard, known as the “jungle”.
Jatta said that on the day of the killing, the leader of the mission, Captain Tumbul Tamba, Jatta and two other soldiers, Alieu Jen and Sana Manjang.
They picked up a car from Jammeh’s residence in the town of Kanifing.
“Tamba was speaking to Jammeh by phone,’’ said Jatta.
“He was saying to him, ‘Yes Sir, Your Excellency’.
“We met a car and Tamba, who was driving, said this is the idiot (Hydara) and he ordered us to shoot.
“I shot at him, my colleagues Alieu Jeng and Sana Manjang also fired.’’
Jatta said he was paid 50,000 dalasis ($1,000) for the hit.
He said he only learned the following day that the target had been Hydara, who also worked for Agence France Presse and Reporters Without Borders.
Tamba died several years ago.
The whereabouts of Jeng and Manjang are not known and they could not be reached for comment.
Gambian investigators have accused Jammeh of several other crimes, including ordering the killing in 2005 of about 50 migrants who he feared had come to overthrow him.
The bodies of the migrants were dumped down a well in neighbouring Senegal.
Gambia’s Justice Minister said in March that Jammeh had personally stolen at least $362 million from the state during his presidency.
Members of Jammeh’s political party have denied such accusations of human rights abuses and corruption.