"The Prime Minister called President-Elect Hollande this evening and congratulated him on his victory," said a spokesman from Cameron's Downing Street office in a statement.
"They both look forward to working very closely together in the future and building on the very close relationship that already exists between the UK and France," it added.
Hollande was elected France's first Socialist president in nearly two decades on Sunday, dealing a humiliating defeat to incumbent Nicolas Sarkozy and shaking up European politics.
The result will have major implications for Europe as it struggles to emerge from a financial crisis and for France, the eurozone's second-largest economy and a nuclear-armed permanent member of the UN Security Council.
Conservative leader Cameron's domestic austerity drive is at odds with the incoming president's belief in government-driven growth and the prime minister backed Sarkozy at the beginning of the election campaign.
Despite a turbulent relationship, Cameron earlier wished Sarkozy luck and said that his counterpart had "achieved great things for his country."
Sarkozy and Cameron clashed over the European fiscal pact, which Britain refused to sign and which Hollande has vowed to renegotiate.
Britain's centre-right media has expressed concern over a Hollande victory after he declared war on the finance industry, which generates huge revenues for Britain.
Hollande called for greater financial markets regulation during a visit to woo French voters in London in February.
In Europe's financial hub, the president-elect tried to play down concerns over his intention to crack down on the financial world, telling one journalist: "I am not dangerous."
Hollande played down the lack of a meeting with Cameron in London, the British leader arguing it was not protocol to meet with presidential candidates.
He did hold talks with Ed Miliband, leader of Britain's opposition centre-left Labour party, and said he had not asked for a meeting with Cameron.
Miliband congratulated Hollande on Sunday's victory and praised the new leader's "determination to help create a Europe of growth and jobs, in a way that is responsible and sustainable".
"This new leadership is sorely needed as Europe seeks to escape from austerity," he added. "I look forward to working together with him in the months and years ahead."