Michael Fallon said the decision to continue deploying around 450 troops followed a planned review of the performance of Afghan security forces and the overall security situation in Afghanistan.
Afghan forces had shown themselves to be "an increasingly professional, competent and dedicated fighting force," he said, and the scope and role of the UK mission were unchanged.
"We will continue to help develop Afghanistan's future military leaders through our work at the Afghan National Army Officer Academy, to build capacity within the Afghan security ministries, and to provide vital support to NATO operations in Kabul," Fallon said in a statement.
The defense minister paid tribute to the 456 UK troops who have died during operations in Afghanistan.
Afghanistan welcomes announcement
said it welcomed Britain's decision to continue its military and economic assistance.
"The cooperation is grounded in shared threats and interests between the two governments and peoples. The government of Afghanistan believes that inasmuch as terrorism threatens the region and the world, joint action against this phenomenon can ensure peace in the region," it said in a statement.
"One of the prerequisites to completely eliminate insecurity and other risks that threaten our country and international partners is the prosperity and economic development of Afghanistan; to that end, the government of Afghanistan thanks its international partners like Britain for their assistance."
Britain is part of NATO's Resolute Support Mission
, which involves 14 member and partner countries and is aimed at providing training, advice and assistance for the Afghan security forces and institutions.
The country formally ended its combat mission in Afghanistan a year ago
, handing over its last remaining base to Afghan forces.
The lowering of the Union Jack flag at the Bastion-Leatherneck coalition base, in Helmand province, marked the end of 13 years of UK combat operations in the country.
Britain's Ministry of Defence said
then that Afghan National Security Forces would take over all former UK bases and operations and that it would support their development as part of the NATO
Fallon's statement follows U.S. President Barack Obama's October 15 announcement
that U.S. troops would remain in Afghanistan at their current levels throughout much of 2016.
"Our forces ... will remain engaged in two narrow, but critical, missions," Obama said,
"training Afghan forces and supporting counter-terrorist operations against the remnants of al-Qaeda."