20 November 2011 Last updated at 19:19
Reporters swamped Mr Rajoy after he cast his vote
PM Jose Luis Rodriguez Zapatero, whose Socialist Party has run Spain since 2004, was not standing again.
With slow growth and almost five million unemployed, the economy dominated the campaign with borrowing rates rising again over the past week.
They rose close to the 7% level which is seen as unsustainable.
An exit poll by state broadcaster RTVE indicated the PP has taken 181 to 185 of the 350 seats in the lower house.
The BBC's Sarah Rainsford, in Madrid, says whoever takes over will have little time to show results.
People are bracing themselves for a new wave of spending cuts and far deeper austerity, she adds.
'Sacrifices ahead'
Voters turned out to choose members of the lower house, the Congress of Deputies, as well as the 208-seat the Senate.
After casting his vote in Madrid, Mr Rajoy said he was "ready for what the Spaniards want".
Reporters swamped Mr Rajoy after he cast his vote
Migel Arias, the Popular Party's campaign co-ordinator, said Spain was "going to make all the sacrifices".
"We have been living as a very rich country," he told BBC News.
"People are used to a very high level of public services and it takes time to them to acknowledge the realisation that we now are a poor country, that we have lots of debts and in order to pay them back we must reduce public expenditure and then we must recover the confidence of the markets."
Alfredo Perez Rubalcaba, the Socialist Party's chosen successor for Mr Zapatero, has accused Mr Rajoy of planning severe cuts to health and education.
"Spain is at a historic crossroads," he told reporters in the Spanish capital.
'Worse and worse'
Analysts say the winner must move quickly to reassure markets that Spain is committed to repaying its debt.
Polls conducted in November suggested the Popular Party would win more than 45% of the vote, some 15% ahead of the Socialists.
It could give the right its biggest win since the end of the Franco dictatorship in 1975.
Correspondents say many are angry with the Socialists for allowing the economy to deteriorate and then for introducing tough austerity measures.
One voter in Madrid, 50-year-old hotel worker Luis Escobar, told Reuters news agency: "Thank God I haven't lost my job. We have to do something.
"What we were doing was not enough, things were just getting worse and worse. The best social policy is to create jobs. The guys in power haven't done anything so if you want things to change you have to do something."
Another voter in the city, 38-year-old local government administrator Antonio Diaz said that without the election, which was called four months early, "the markets would have changed the government as they did in Greece and Italy".
