Mr Miliband's visit is the first by a British foreign minister for five years
British Foreign Secretary David Miliband is due to visit Russia next month in an apparent attempt to patch up strained relations with Moscow.
British officials said Mr Miliband had been invited by his counterpart, Russian Foreign Minister Sergei Lavrov.
Ties between Russia and the UK have been strained in recent years, most notably after the 2006 murder of former KGB spy Alexander Litvinenko in London.
Russia has refused British requests for the extradition of the main suspect.
Relations were worsened when Moscow ordered the closure of British Council offices in Russia due to alleged tax irregularities.
There have also been tensions over spying claims and a struggle over BP's interests in Russia.
Meanwhile, the UK has expressed concern over Russian human rights.
In a statement, the British Foreign and Commonwealth Office said: "The Foreign Secretary welcomes this opportunity to continue to engage with Russia on the major global challenges we all face in which Russia plays a key role.
"These include the Middle East, Afghanistan, Iran, non-proliferation of weapons of mass destruction, climate security and tackling the global economic crisis."
The Foreign Office said Mr Miliband would meet a range of politicians, business leaders and representatives of civil society.
His visit is due to be the first by a British foreign secretary in five years.