The BBC understands 10 officers will provide logistics and intelligence training in a UK and French operation.
Mr Hague said it was compatible with the UN resolution on Libya, which ruled out foreign military ground action.
He stressed that the officers would not be involved in any fighting and the move was needed to help protect civilians.
Support and advice The UN Security Council resolution, passed in March, authorised a no-fly zone over Libya.
Mr Hague said: "The [UK] National Security Council has decided that we will now move quickly to expand the team already in Benghazi to include an additional military liaison advisory team. This contingent will be drawn from experienced British military officers.
"These additional personnel will enable the UK to build on the work already being undertaken to support and advise the NTC [opposition National Transitional Council] on how to better protect civilians.
"In particular they will advise the NTC on how to improve their military organisational structures, communications and logistics, including how best to distribute humanitarian aid and deliver medical assistance.
"In doing so, we will coordinate closely with other international partners also assisting the NTC."
Body armour The officers will be wearing civilian clothing, not uniforms, but are likely to carry sidearms.
The announcement comes as hundreds of people are feared dead in the bombardment of the town of Misrata by pro-Gaddafi forces. William Hague: "This is not British ground combat forces going in...this is fully in-line with the UN resolution"
The UK has already supplied body armour and telecommunications equipment to help the rebels.
On Monday, International Development Secretary Andrew Mitchell said the UK would provide £2m to help civilians flee Misrata by boat.
Mr Hague said: "We have stepped up our contribution to international efforts to relieve the humanitarian crisis in Libya, in particular in Misrata, and a UK diplomatic team led by Christopher Prentice has been liaising closely with the opposition in Benghazi."
French Foreign Minister Alain Juppe has said France is opposed to the idea of sending coalition ground troops into Libya, even special forces to guide air strikes, to break the military stalemate.
'Mission creep' Former Liberal Democrat foreign affairs spokesman Sir Menzies Campbell warned against becoming bogged down in Libya, in similar fashion to what happened to the US in Vietnam.
He said: "Sending advisers for a limited purpose is probably within the terms of [United Nations] Resolution 1973, but it must not be seen as a first instalment of further military deployment.
"Vietnam began with an American president sending military advisers. We must proceed with caution."
Labour MP David Winnick, who backed last week's demands to recall Parliament from the Easter recess so MPs could debate the Libya situation, criticised the deployment of British officers.
He said: "However much one despises the brutality of the Gaddafi clan which rules Libya, the fact remains that there is a danger of mission creep.
"There is a civil war in Libya and this is a big escalation of Britain's involvement. I don't think there is an appetite in Britain for military intervention.
"Having been engaged in two wars in nine years in Muslim countries, it would be unwise to become involved in a third."
'Precision firepower' Meanwhile, British military chiefs have been giving details of the latest action by the RAF to enforce the no-fly zone.
Maj Gen John Lorimer said Tornado and Typhoon aircraft attacked rocket launcher vehicles and light artillery observed firing on Misrata, and a second pair of RAF planes destroyed a gun and tank on a transporter.
Tomahawk cruise missiles were also fired by the nuclear-powered submarine HMS Triumph.
Maj Gen Lorimer said: "It will take time for the full impact of these attacks to become clear.
"But they do illustrate in the clearest manner Nato's resolution to take all necessary action to safeguard wherever possible the Libyan people under threat of attack and its ability to strike, with sophisticated targeting and effective precision firepower, at the heart of the apparatus used by Colonel Gaddafi to terrorise the civilian population."
The World Food Programme said it had started moving supplies through a new humanitarian corridor into western Libya, with the first convoy crossing from Tunisia on Monday.
It was loaded with enough wheat flour and high-energy biscuits to feed 50,000 people for 30 days.
The food will be delivered to several Libyan cities, although not Misrata which is said to be critically short of supplies.