The poll was held five months after Mr Zelaya was forced out at gunpoint, with an interim government taking over.
Mr Lobo is seen as a unifying figure. He won 56% of the vote, with over 60% of registered voters taking part.
A clear winner and high turnout were what the interim government were hoping for to give the election legitimacy.
But regional powers Argentina and Brazil have said they will not recognise any government installed after the election, arguing that to do so would legitimise the coup which ousted an elected president, and thus set a dangerous precedent.
Brazilian President Luis Inacio Lula da Silva also said that Mr Zelaya will remain in its embassy in the Honduran capital Tegucigalpa - where he has been living since he secretly returned to the country in September - until the government gave assurances for his safety.
The US, meanwhile, said it would accept the election results.
Mr Lobo comes from the centre-right opposition National Party, and was defeated by Mr Zelaya in the last presidential election in 2005.
The BBC's Stephen Gibbs in Tegucigalpa says although many members of the current interim government belong to the rival Liberal Party, they are expected to welcome the result.
Mr Zelaya is also a Liberal, but alienated many in his own party when he moved the country closer to left-wing leaders such as Venezuelan President Hugo Chavez and Bolivian President Evo Morales.
'Important step'
The US said Sunday's vote was important.
"Significant work remains to be done to restore democratic and constitutional order in Honduras, but today the Honduran people took a necessary and important step forward," State Department spokesman Ian Kelly said in a statement as the results were coming in.
The Honduran government has tried to portray this election as a nationwide demonstration that the country is on a democratic path, after five months of political crisis.
Mr Zelaya described the vote to elect his replacement as a "fraud" and called on his supporters to abstain. He has not yet commented on the results.
During the day's voting, several hundred protesters against the election gathered in the city of San Pedro Sula.
They were dispersed by security forces using tear gas.
Mr Lobo said he would encourage regional powers to accept the result of the election.
"We are prepared to approach them and ask them to understand that there is a government which was elected, that it is the precise will of Hondurans at the ballot box, that it is a democracy and we should all respect the leadership of countries," he said, according to Reuters news agency.
The political crisis and election have divided the region, with Costa Rica, which has long been the mediator between the two sides in the crisis, saying it would accept the result, but other Latin American countries opposing the vote.
Congress is due to vote on Mr Zelaya's reinstatement on 2 December. His term ends on 27 January.
Mr Zelaya was forced into exile on 28 June after trying to hold a vote on whether a constituent assembly should be set up to look at rewriting the constitution.
His critics said the vote, which was ruled illegal by the Supreme Court, aimed to remove the current one-term limit on serving as president and pave the way for his possible re-election.
Mr Zelaya has repeatedly denied this and some commentators say it would have been impossible to change the constitution before his term in office was up.
