The US, for its part, has been enforcing a blockade of Iranian ports to exert pressure on Tehran to agree to its terms – a move that has infuriated Iran.
Some 20% of the world’s oil and liquefied natural gas uses the crucial waterway, whose blockage has sent prices soaring globally.
A ceasefire has been in place between the US and Iran since April, but US President Donald Trump has said it is on “massive life support”.
Both sides have accused the other of launching attacks in the strait.
There is already more than 1,000 British personnel deployed in the region as part of existing defensive operations, including counter-drone teams and fast jet squadrons, the ministry said.
The Ministry of Defence said the multinational mission – which was announced last month by the UK and France – is strictly defensive and aimed at restoring confidence for commercial shipping along the Strait of Hormuz.
It said the contribution is backed by £115m new funding for mine-hunting drones and counter-drone systems.
“With our allies, this multinational mission will be defensive, independent, and credible,” Healey said in a statement.
Under the plan, HMS Dragon – the air defence destroyer that is already on its way to the Middle East – will also “be ready for any mission” to secure the strait, the MoD said.
It added that another British ship, the RFA Lyme Bay, continues to be upgraded by with new equipment, if required for operations in the strait.