Farrakhan has been accused of preaching racism
Home Office Minister Beverley Hughes said the government was "very disappointed" by Tuesday's ruling and would be considering an appeal.
Groups opposed to racism and anti-Semitism also attacked the judge's decision, saying Mr Farrakhan's visit had the potential to threaten racial harmony in the UK.
The head of the Nation of Islam has been dubbed a "black racist" by opponents after using inflammatory language about Jews and whites in speeches.
But Mr Farrakhan told BBC Radio 4's PM programme: "I really don't think that there is any evidence in the 47 years of my ministry in the USA and in other parts of the world that any violence follows my speeches or follows my teaching."
He said Islam was not a racist religion, adding that his message during his visit to Britain would be based on the themes of "atonement, reconciliation and responsibility ... a theme that is much needed in the UK".
His supporters applauded the overturning of the ban imposed by successive home office ministers, which could mean a visit by Mr Farrakhan in the autumn.
US civil rights leader the Rev Jesse Jackson told the BBC that Mr Farrakhan was coming to Britain "as a source of reconciliation and peace".
'Racially divisive views'
But the 67-year-old leader will not be able to come to the UK until after the judge outlines his reasons for his decision on 1 October.
Mr Farrakhan, who is suffering from cancer, challenged last November's decision by the then Home Secretary Jack Straw to maintain the ban.
In November Mr Straw justified upholding the ban on the grounds that Mr Farrakhan had expressed "anti-Semitic and racially divisive views".
Lawyers for Mr Farrakhan argued the ban was unlawful as it interfered with the leader's right to speak with his UK supporters about spiritual values for the black community.
And they said the ban was contrary to the Human Rights Act and the common law.
On Tuesday, David Liddington, shadow home affairs spokesman, shared the government's dismay.
"I find it extraordinary that the judge is not prepared to give his reasons for his decision for a further two months," he said.
Lord Janner of the Holocaust Education Trust said the black leader "had made odious attacks on Jews" and described Hitler as "a great man".
'Reconciling differences'
But following Tuesday's ruling, Rev Jackson said:
"Whether it is the British leadership and the IRA sitting down to talk, or
the ANC talking to the Afrikaaners, or the PLO talking to the Israelis, we can
only reconcile our differences when we allow to talk with each other and seek
resolution."
"He says he wants to come to Britain as a source of reconciliation and peace and that would be the tone of his remarks, and I hope he honours that position."
Hilary Muhammad, UK spokesman for the Nation of Islam also welcomed the ruling.
"Now the citizens of UK will have a chance in the near future to see, hear and judge the honourable Minister Louis Farrakhan for themselves," he said.