"The relationship between the United States and the United Kingdom is vital to our prosperity and security," said Brown.
"Barack Obama ran an inspirational campaign, energising politics with his progressive values and his vision for the future."
Other European leaders also hailed the Democrat's landslide victory on Tuesday.
French President Nicolas Sarkozy said Obama's "brilliant" victory would bring new energy to the relationship between Europe and the US, notably strained during the administration of current President George W Bush due to differences over Iraq and Afghanistan.
"By choosing you, the American people have chosen change, openness and optimism," Mr Sarkozy wrote in a letter to Obama. "At a time when we must face huge challenges together, your election has raised enormous hope in France, in Europe and beyond."
German Chancellor Angela Merkel described Obama's victory as "historic", whilst Russia's Deputy Foreign Minister, Grigory Karasin, said he expected a "fresh approach" from the US to relations with Russia.
In Kenya, the home country of Obama's late father and other relatives, there was widespread jubilation.
President Mwai Kibaki declared Thursday a public holiday, saying, "This is a momentous day not only in the history of the United States of America, but also for us in Kenya. The victory of Senator Obama is our own victory because of his roots here in Kenya. As a country, we are full of pride for his success."
US civil rights campaigner, the Rev Jesse Jackson was reduced to tears of joy over Obama's victory. "America is changing for the better," he said.
