Troops from the Economic Community of West African States (ECOWAS) have entered The Gambia without any resistance from the country’s military.
The troops have secured the State House, which is the seat of government.
The ECOWAS troops entered The Gambia after midnight, hours after last minute talks between Mauritania President Mohamed Abdel Aziz and Mr Jammeh fell through.
The country’s President-elect Adama Barrow is expected to be sworn in today, January 19.
He is currently waiting in neighbouring Senegal to be flown in after the operation to remove Jammeh is over.
A statement from the Flagstaff House Wednesday said President Akufo-Addo approved and authorized the deployment of a combat team of Two Hundred and Five (205) troops, backed with the appropriate logistical equipment, to support the ECOWAS troops.
Senegal gave him a midnight GMT deadline to quit, and Nigeria has sent an air force unit to Senegal in support of the possible intervention. Wednesday was meant to be his last day in office, but parliament has granted him three more months in the post.
It effectively stops successor Adama Barrow from being sworn in on Thursday.
His shock victory in the December 1 election plunged The Gambia into crisis. West African countries are seeking UN backing to intervene militarily to eject Mr Jammeh, who has ruled The Gambia since taking power in a bloodless coup in 1994.
Meanwhile, thousands of UK and Dutch tourists are being evacuated from the tiny West African state, which is popular with European holidaymakers because of its beaches.
Why is Mr Jammeh refusing to leave office?
The Gambia regularly held elections, which he won until last year. Mr Jammeh has said there were irregularities in the election process, including the turning away of some of his supporters from polling stations, and errors made by the electoral commission.
The commission accepted that some of the results it initially published contained errors, but said Mr Barrow had still won.
Mr Jammeh has said he will stay in office until new elections are held. Retaining power would also ensure he was not prosecuted in The Gambia for alleged abuses committed during his rule.
The US state department urged Mr Jammeh to peacefully transfer power to Mr Barrow on Thursday. “Doing so would allow him to leave office with his head held high and to protect The Gambian people from potential chaos,” spokesman John Kirby said.