The mission is to involve assets already positioned in the region, such as the HMS Duncan and HMS Montrose warships, and Britain has offered to head one of the mission's task groups.
Those two vessels "have already successfully accompanied 47 merchant ships," the statement said.
"The UK is determined to ensure her shipping is protected from unlawful threats and for that reason we have joined the new maritime security mission in the Gulf," Defence Secretary Ben Wallace said.
He called Britain's involvement "a sign of our commitment" to British-flagged vessels.
Iran impounded the British-flagged Stena Impero and the Panama-flagged MT Riah in the Strait of Hormuz last month, causing a major flare-up in tensions with Britain and the United States.
The seizures were seen as retaliation after British troops helped capture the tanker Grace 1, which was carrying Iranian oil, allegedly to Syria in violation of EU sanctions, on July 4 off the British territory of Gibraltar.
British Foreign Secretary Dominic Raab has spoken to partners around the world to encourage them to join the maritime mission, the Ministry of Defence said.
"It is vital to secure the freedom for all international shipping to navigate the Strait of Hormuz without delay, given the increased threat," Raab was quoted as saying in the statement.
Iranian state media said the country had seized another oil tanker in the Gulf on Sunday.
The US has also blamed Iran for two attacks using explosives, which damaged oil tankers in the Gulf in May and June. Tehran has denied the allegations.
Meanwhile, the German government is actively pushing for a European Union observer mission to protect shipping in the Gulf, Foreign Minister Heiko Maas said on a visit to the Polish border on Monday.
Last week, Germany made clear that it would not participate in a mission led by the United States to safeguard shipping in Strait of Hormuz, through which one fifth of the world's oil passes.
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