Finland's communication minister Suvi Linden explained the thinking behind the legislation: "We considered the role of the internet in Finns everyday life. Internet services are no longer just for entertainment.
"Finland has worked hard to develop an information society and a couple of years ago we realised not everyone had access," she said.
It is believed up to 96% of the population are already online and that only about 4,000 homes still need connecting to comply with the law.
In the UK internet penetration stands at 73%.
The British government has agreed to provide everyone with a minimum 2Mbps broadband connection by 2012 but it is a commitment rather than a legally binding ruling.
"The UK has a universal service obligation which means virtually all communities will have broadband," said a spokesman for the Department for Culture, Media and Sport.
Making broadband a legal right could have implications for countries that plan tough action on illegal file-sharing.
Both the UK and France have said they may cut off or limit the internet connections of people who persistently download music or films for free.
The Finnish government has adopted a more gentle approach.
"We will have a policy where operators will send letters to illegal file-sharers but we are not planning on cutting off access," said Ms Linden.
A poll conducted for the BBC World Service earlier this year found that almost four in five people around the world believed that access to the internet is a fundamental right.