"His resignation shows that Gaddafi`s regime, which has already seen significant defections to the opposition, is fragmented, under pressure and crumbling from within," Hague said as Koussa was being questioned after his arrival.
But in a surprise move, Hague asserted that the Libyan leader was not being offered immunity from British or international justice.
Moussa Koussa is one of the most senior figures in Gaddafi`s government and his role was to represent the regime internationally, but during questioning he said that he was no longer willing to represent Gaddafi.
BBC said the Libyan Foreign Minister has arrived in UK on what is believed to have been a British military plane.
But a British foreign office spokesperson said, Koussa who is in early 60s had arrived in Farnborough airport, west of London, last night.
"He told us that he has resigned his post and had come from Tunisia where he had crossed over two days back," the spokesperson said.
Describing the defection as "encouraging signs", Hague said, "We are asking all those around Gaddafi to abandon him and embrace a better future for Libya that allows political transition and real reforms that meet the aspirations of the people.
"Gaddafi must be asking himself who will be the next to abandon him," the British Foreign Secretary said. His arrival in the UK comes as Libyan rebels are reported to be in full retreat from recently captured town along the country`s eastern coast.
Libya`s Interior and Justice ministers resigned earlier in the conflict and join the rebels fighting in the east.
Libyan exiles in London said that Koussa had been Gaddafi`s right hand man for years, running intelligence, and running the Lockerbie bomber negotiations.
Earlier, Tunisian government official said that Koussa was accompanied by Libya`s Vice Minister Abdelati Laabidi, who returned to Libya from Tunisia.
Addressing concerns over the defection of the controversial Libyan foreign minister to the UK, Hague told newsmen this morning that he had been communicating with Koussa over recent weeks.
"He has been my channel of communication to the regime in recent weeks and I have spoken to him several times on the telephone.
Questions were earlier raised about Koussa`s whereabouts after Tunisian news agency TAP reported he had entered that country, but gave no reasons for his move.
A Libyan government spokesman later claimed he had not defected and was merely on a "diplomatic mission", but declined to say where he was going. Libya`s deputy foreign minister Khalid Kaim dismissed the reports as "nonsense".
But within hours the Foreign Office confirmed he was seeking refuge and encouraged further regime defections.
Azeldin El Sharif, president of the British Libyan Solidarity Campaign, told Sky News it was a "very significant" step forward for the opposition`s cause.
He said: "This is an absolutely massive loss for Gaddafi."
According to reports, Koussa defected after pressure from Britain`s intelligence agency MI6.
Koussa`s decision to abandon Gaddafi is being considered a diplomatic coup for David Cameron, who has urged the Libyan leader`s henchmen to jump ship.
But his arrival could also present the government with a headache since many will find his presence in the UK distasteful.
Libyan exile groups branded Koussa `the envoy of death` for his alleged role in the 1980s directing terrorist atrocities across Europe and organising the murder of exiled opponents of the Gaddafi regime.
In 1980, he was expelled as Libya`s envoy in London for publicly backing the murder of overseas dissidents and threatening to back the Provisional IRA unless they were handed over.
As the former head of his country`s intelligence agency, he is thought to hold key information on the murder of British police officer Yvonne Fletcher outside the Libyan embassy in London in 1984.
He was later labelled `the father of Lockerbie` for masterminding the destruction of Pan Am Flight 103 in 1988.