This includes as many as 40 military advisers who will train soldiers in Mali, and 200 British soldiers to be sent to neighbouring African countries, also to help train the Malian army.
French-led forces are continuing their offensive against Islamist militants who seized northern Mali last year.
International donors have pledged $455.53m (£289m) to tackle militants.
The 330 military personnel comprise 200 soldiers going to West African nations, 40 military advisers to Mali, and 90 support crew for a C-17 transport aircraft and a Sentinel R1 surveillance plane. None will have a combat role.
A conference taking place in Brussels is expected to decide which countries will contribute troops for an EU military training mission for Mali and discuss details of the mission.
Meanwhile, French-led troops are consolidating their position in the historic Malian city of Timbuktu after seizing it from Islamist extremists. They are then expected to focus on the last rebel stronghold, Kidal. They seized Gao, northern Mali's biggest city, on Saturday.
In a separate development, Downing Street said UK Prime Minister David Cameron was to visit neighbouring Algeria on Wednesday.
The trip comes in the wake of a hostage crisis that left four Britons and a UK resident dead and two Britons believed dead. During the siege, one statement purporting to be from the hostage-takers called for an end to the French military intervention against Islamist militants in Mali.
Detailing in the House of Commons the "extended support" the UK will offer France, Defence Secretary Philip Hammond said it would:
The UK also offered to set up a combined joint logistics HQ in Mali. However, so far the French have declined this offer.
UK shadow defence secretary Jim Murphy said there were concerns about "mission creep".
"The UK commitment to Mali has grown from lending the French two transport aircraft to the deployment of perhaps hundreds of troops to the region," he said.
"UK trainers may be non-combat but that does not mean they are without risk."
But Mr Hammond stressed: "It is not our intention to deploy combat troops. We are very clear about the risks of mission creep.
By Jonathan BealeDefence correspondent, BBC News
So does this move by the UK signal a new era of defence co-operation - the fruit of the defence treaty signed by Mr Cameron and the then French President Nicholas Sarkozy at Lancaster House just a few years ago? Well, yes and no.
British and French forces have already carried out a number of joint military exercises. They've also worked together in battle - most recently joining forces in the overthrow of Libya's Colonel Gaddafi.
But Libya was fought under the Nato umbrella. And Mali is clearly being led by the French. It's not a truly joint operation, or a sign that in the future Britain will always intervene with the French, or vice versa.
It's more an old fashioned "coalition of the willing", based on the shared threat posed by Islamic radicals. Ultimately British and French commanders are not sitting down together in a joint operations room calling the shots.
And when British troops do arrive on the ground in Mali - in relatively small numbers - they'll be working as part of an EU mission.
"We have defined very carefully the support that we are willing to provide to the French and the Malian authorities."
Number 10 is also considering who will provide "force protection" for the military advisers. At present, it is envisaged the force protection will not be provided by British soldiers. It is possible existing French forces in Mali could be used.
Former defence minister Sir Nick Harvey warned the number of personnel involved could rise if the UK had to provide its own force protection.
"If they (the military advisers) are spread out in different locations providing technical advice to different aspects of the Malian forces then those numbers will begin to climb quite rapidly," he said.
Military analyst Col Mike Dewar said the initial UK support was short-term but its latest offer of help constituted a "much more long-term plan".
It could take "years" for the British troops to make a difference to the "ill-trained" Malian army, he said.
The former head of the Army, General Sir Mike Jackson, backed the government's position but warned that nations involved may face a "protracted guerrilla warfare".
The UK is to deploy about 330 military personnel to Mali and West Africa to support French forces, No 10 has said.