The HMS Diamond, a Type 45 destroyer, will conduct operations to ensure freedom of navigation, reassure merchant vessels and ensure the safe flow of trade, the defence ministry said.
"It is critical that the UK bolsters our presence in the region, to keep Britain and our interests safe from a more volatile and contested world," said Defence Secretary Grant Shapps.
The deployment follows the outbreak of conflict between Israel and Hamas and the seizure of an Israeli-linked cargo vessel by Iranian-backed Yemeni Huthis in the Red Sea on November 19.
The Huthis have launched a series of drone and missile strikes targeting Israel since Hamas militants poured over the border into Israel on October 7, killing 1,200 people, mostly civilians, and kidnapping about 240.
The ministry said around 50 large merchant ships each day pass through the Bab-el-Mandeb, connecting the Red Sea to the Gulf of Aden, while around 115 major merchant ships pass through the Strait of Hormuz.
The waters of the Gulf, it said, are vital routes for merchant shipping, including for tankers carrying much of the UK's supply of liquefied natural gas.
Royal Navy vessels have been permanently deployed to the region since 1980 and since 2011 have fallen under "Operation Kipion", the name used for the UK's maritime presence in the Gulf and the Indian Ocean.
"Today’s deployment will strengthen the Royal Navy's patrols, help to keep critical trade routes open and prove that our commitment to regional security not only endures but enhances," Shapps said.
The vessel will join the frigate HMS Lancaster which deployed to the region last year, as well as three mine hunters and a support ship.