Mr Romney blamed Mr Obama for the economic woes frustrating voters, like federal spending and unemployment during a speech in New Hampshire.
If elected, he said he would make the US the world's top job creator.
The wealthy businessman is the current frontrunner in the Republican field.
BBC North America editor Mark Mardell, in New Hampshire, says Mr Romney - a tremendous fund raiser and serious seasoned campaigner - is clearly the man for others to beat.
But he is yet to convince conservatives he really is one of them and yet to convince the media that he has the flair and panache need to maintain interest and momentum, our correspondent adds.
'Failed America'
The Republican multi-millionaire was beginning his campaign in the state of New Hampshire, an important early-voting state which is expected to hold its primary election to pick a candidate in February 2012.
Analysts say Mr Romney's speech, which was released ahead of his announcement, is also tailored to appeal to conservatives who hold great sway in choosing the Republican presidential nominee in Iowa and South Carolina.
"Government under President Obama has grown to consume almost 40% of our economy," Mr Romney said.
"At the time, we didn't know what sort of a president he would make.... Now, in the third year of his four-year term, we have more than promises and slogans to go by. Barack Obama has failed America."
Mr Romney has said, if elected, he would balance the federal budget and limit federal spending at 20% of gross domestic product.
Mr Romney's announcement on Thrusday marks the second time he will be running for the Republican nomination.
He lost the party's 2008 nomination race to Arizona Senator John McCain and has spent the four intervening years building support within the party and preparing for the 2012 race.
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