The UK prime minister said the effects of the two countries' economic bailout packages would be "magnified" if they worked closely together.
The BBC's political Editor Nick Robinson says the prime minister will hold half an hour of personal talks with Mr Obama on Tuesday in Washington.
Mr Brown will be the first European leader to meet President Obama.
He will also become the fifth British prime minister to address Congress when he does so on Wednesday.
Before setting off for Washington, Mr Brown told TalkSport radio he was "impressed" by Mr Obama: "I think first of all to meet him [Mr Obama] as a person, you cannot but be impressed by his demeanour, his determination, not just his fluency, but his sympathy for the causes he represents.
"I think the impression he has given of America to the world is transformative, because he is a black man who has won the presidency, who is living in the White House that was built by slaves."
He added: "I think people's view of America is changing as a result of that."
Although talks will be dominated by the recession, the two leaders are also expected to discuss the situation in Afghanistan, Iraq and the Israeli-Palestinian conflict.
Protectionism fear
Mr Obama was facing "very difficult" economic decisions after taking office in the middle of a crisis and "doing similar things to what we are doing in Britain", Mr Brown said.
Following an EU summit at the weekend, the prime minister said he would take a "clear message" from European leaders that "bold global action" was needed to tackle the economic crisis.
His address to Congress is expected to compare the battle against the global recession to the fight against European fascism in the 1940s.
Former assistant secretary of state, James Rubin, said one of the current fears was protectionism.
"Everyone who's an international economist is worried about this sort of thing," said Mr Rubin.
"But everyone who's a politician knows that people are going to have to take care of their own in a time of crisis.
"That doesn't mean there isn't going to be plenty of trade and plenty of international economic cooperation. But when you have a crisis like this people have a tendency to look first to their own constituents."
The EU and Canada have warned that a "Buy American" clause in the US economic recovery package could promote protectionism.
It seeks to ensure that only US iron, steel and manufactured goods are used in construction work funded by the bill - but has included a pledge to respect international trade obligations.
Mr Brown's meeting with Mr Obama comes ahead of the G20 summit of the world's biggest economies in London next month - in which Mr Brown has said it is vital that world leaders "take the big decisions necessary to secure our economic future".
