Under Ed Miliband, Labour had said they would not back a referendum bill.
Writing in the Sunday Times, Ms Harman and shadow foreign secretary Hilary Benn said voters wanted a say on membership, but said they would campaign for a yes vote.
“We have now had a general election and reflected on the conversations we had on doorsteps throughout the country.
The British people want to have a say on the UK’s membership of the European Union. Labour will therefore now support the EU referendum bill when it comes before the House of Commons.
“The Labour Party doesn’t want to see the UK stumble inadvertently towards EU exit.
We will make the case for our continued membership.Harriet Harman
“We will make the case for our continued membership. The notion that Britain’s future and prosperity and security lies shutting itself off from this market and a world that is increasingly interdependent makes no sense.
“And in an age of powerful trade blocs, with the growing economies or Asia and Africa, we have more power by being in the EU than we could ever hope to have by acting alone. That is the argument we will make in this referendum, as the British people make their decision.”
Ms Harman said the UK would just be a “small country” outside the EU, but said she accepted some of Mr Cameron’s concerns about the need for change.
She told BBC1’s Andrew Marr Show: “I think that we have got the same concerns that you should contribute into the benefits system before you take out.
“We have got additional concerns about making sure there is not underpayment of the minimum wage and that there is a living wage so that people don’t feel undercut in their workplace in terms of pay.
“If we were outside of Europe we would be a small country, outside of those big, continental building blocks around the globe.”
Shadow Europe Minister Pat McFadden told Channel 4 News Labour frontbenchers would be arguing for Britain to remain in Europe alongside other voices from outside politics and business leaders.
He said the party would warn voters not to “retreat into nationalism and nostalgia”, adding: “Britain’s place in the world is at stake in this debate.”
Mr McFadden said he wanted to see 16- and 17-year-olds given the vote in an EU referendum, as they were in the vote over Scottish independence last year.