The troops will be sent to the southern Afghan province of Helmand, where six British soldiers have died in attacks in the past few weeks.
The reinforcements will bring the total number of British troops in Afghanistan to more than 4,500 by October. They will assist in security and reconstruction efforts, said Des Browne, the British defence secretary.
"We have taken casualties, but we have overmatched the opposing forces every single time we have faced them,"
Browne said. "They have tried to block our mission and failed."
Senior military commanders say that British troops - who began arriving in Helmand in February - have faced more resistance than they had initially anticipated, although Browne denied that this was the case.
Officials say many of the additional troops will remain for at least six months, as Nato prepares to take charge of the peacekeeping mission across southern Afghanistan at the end of the month.
The Nato mission, intended to extend the authority of Afghanistan's government under President Hamid Karzai, will replace the US-led operation launched after the September 11 attacks in 2001.
'No strategic threat'
The recent violence has surprised the Afghan government and its Western backers and raised fears that Nato forces in the south risk being sucked into a war.
Condoleezza Rice: The Taliban are
"If we have thought that the Taliban would not recover from their defeat in 2001 we were wrong," said Tom Koenigs, United Nations special representative for Afghanistan.
"They have recovered and they get help through international terrorist networks."
The US-led coalition has responded with offensives and hundreds of Taliban fighters have been killed in the past few months, the US says.
On Monday, Condoleezza Rice, the US secretary of state, said that people should be very careful "not to confuse what is happening in the south with a strategic threat to the Afghan government".
The Taliban are "losing hugely in having confronted, now, coalition forces in that part of the country," she said.