And more are likely to be called up in the next few weeks.
The government says it is important to be prepared for a war with Iraq - even though that may never happen.
A total of 40,000 part-time volunteer soldiers are in the Territorial Army.
But the British Army as a whole has four times as many troops.
The government is also sending a Royal Navy task force, led by HMS Ark Royal, to the Gulf.
Other ships include three destroyers, a frigate, four auxiliary vessels, anti-mine ships and a submarine.