Defence Secretary Sir Michael Fallon made the announcement as his visited Harland and Wolff shipyard in the city, where the Navy's last HMS Belfast was built prior to World War Two.
The ship will be one of eight new Type 26 frigates joining the Navy's fleet.
It will be used to protect the UK's nuclear submarines and aircraft carriers.
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One of the "City Class" frigates has already been christened HMS Glasgow. They are due to enter service in the mid 2020s.
"I'm hugely proud that the second name announced of our eight cutting-edge new Type 26 frigates will be HMS Belfast," said Sir Michael.
"She and her sister ships will form the backbone of our Navy well into the 2060s, keeping us safe by protecting the country's nuclear deterrent and new aircraft carriers.
"It's apt to name this ship at the famous site which built the very first HMS Belfast. Thanks to our ambitious new National Shipbuilding Strategy, this shipyard once again has the chance to be involved in building a British warship thanks to the competition to build a new class of light frigates for our growing Royal Navy."
The original HMS Belfast, which took part in the Arctic campaign and the Normandy landings, is now a floating museum permanently docked in London. It will now be renamed "HMS Belfast 1938" to avoid confusion.
Diane Lees, director general at Imperial War Museums, said: "IWM is delighted that the name HMS Belfast will return again to the Royal Navy's front line as a major warship.
"We welcome the opportunity this will bring for our internationally significant museum to have a close affiliation with the new Belfast, enabling a powerful link between the Royal Navy's past and present."
Admiral Sir Philip Jones, First Sea Lord and Chief of Naval Staff, said: "The City class theme has been chosen for the Type 26 frigates in order to reaffirm the bond between the Nation and its Navy.
"We want to honour some of the great centres of industry and commerce in all parts of the United Kingdom, and few cities have such a rich maritime heritage as Belfast."