The transfer follows Britain's agreement last year to withdraw all but 500 of the 4,100 troops it had stationed in Iraq ahead of its complete military withdrawal from the country in July.
The 500 remaining British soldiers will train Iraqi forces, and the Iraqi Navy in particular.
After the US, Britain sent the largest contingent of soldiers to support the 2003 invasion of Iraq.
British troops transferred the responsibility of operating Basra's civilian airport to Iraqi authorities Jan 1, but the British military retained control of the military base next to the airport. Control of that base will now pass to the US military.
Though calm has largely returned to Basra, the base has frequently been the target of rocket attacks.