Mr Ryan, 42, is a Wisconsin congressman and chairman of the House of Representatives budget committee.
BBC North America editor Mark Mardell says the decision is a bold and ideological choice.
The Obama campaign said Mr Ryan stood for “flawed” economic policies that would repeat “catastrophic” mistakes.
Mr Romney formally unveiled his running mate before hundreds of cheering supporters at the retired battleship USS Wisconsin in Norfolk, Virginia.
In a slip of the tongue, the former Massachusetts governor introduced Mr Ryan as “the next president of the United States”, before correcting himself to say he meant vice-president.
Mr Ryan told the crowd that he and Mr Romney would “restore the greatness of this country”.
“Mitt Romney is a leader with the skills, the background and the character that our country needs at a crucial time in its history,” Mr Ryan said.
“Following four years of failed leadership, the hopes of our country, which have inspired the world, are growing dim, and they need someone to revive them. Governor Romney is the man for this moment.”
Prompting one of the loudest cheers from onlookers, he said: “Our rights come from nature and God, not from government.”
Mr Romney, 65, is launching a bus tour through four key swing states that he needs to win in November’s election: Virginia, North Carolina, Florida and Ohio.
In a little over two weeks’ time, he will be formally confirmed as the Republican nominee at the party convention in Tampa, Florida.
But recent opinion polls suggest a close race between Mr Romney and Democratic President Barack Obama, with Mr Obama tending to have a slight lead in most surveys.
Analysts say Mr Romney needs to regain momentum after a series of pro-Obama campaign advertisements attacking his record.
Correspondents say Republican leaders were concerned over the state of Mr Romney’s campaign, and had urged him to pass over reliable – but not particularly inspiring – figures such as Ohio Senator Rob Portman and former Minnesota Governor Tim Pawlenty, to pick Mr Ryan.
Mr Ryan is best-known for a controversial alternative budget which he produced to counter President Obama’s plans in 2011 and 2012.
Known as the Path to Prosperity, it delighted the Tea Party, an anti-tax, limited-government, grassroots Republican movement.
The plan proposed reducing taxes, pensions and food aid, and overhauling government-funded healthcare.
In all, it projected spending cuts of $5.3 trillion (£3.4 trillion) over a decade.
The Wisconsin congressman rejected criticism that his proposal would harm lower-income groups, saying it would instead create jobs and reduce inefficiency.
Mr Ryan chairs the budget committee in the Republican-controlled House of Representatives, and is seen as likely to add electoral firepower on what are expected to be the key election issues – jobs, the economy and the budget deficit.
Analysts say that as a staunch conservative, he could counteract some scepticism about Mr Romney’s political past as governor of the traditionally liberal state of Massachusetts.
But the Obama campaign said Mr Romney’s choice showed a commitment to “budget-busting tax cuts” for the wealthy and “greater burdens” on the middle class and elderly.
“As a member of Congress, Ryan rubber-stamped the reckless Bush economic policies that exploded our deficit and crashed our economy,” Obama’s campaign manager Jim Messina said in a statement.
Democrats also pounced on the Ryan budget plan’s proposed cuts to Medicare, the federal healthcare programme for the elderly.
Source: BBC News