Mulino was one of the favourites for the presidency after he stepped in to replace Martinelli on the ballot when the popular former president was barred from running due to a money laundering conviction.
"I promise to the country at this time to put together, to establish, a government of unity as soon as possible," Mulino said on Sunday after electoral officials video called him to confirm he had won the presidency.
Earlier, Mulino supporters waved flags, clapped and cheered inside the campaign headquarters as results trickled in. "Martinelli, friend, the people are with you," supporters shouted.
In a strange election campaign, Martinelli played a key role drumming up support for Mulino from Nicaragua's embassy in Panama's capital, where he sought asylum. Many voters saw Mulino as a proxy for Martinelli, though opponents called him a puppet of the former president.
Nicaragua granted Martinelli asylum but Panamanian authorities have blocked him from leaving the country. Mulino visited Martinelli at the embassy after casting his vote on Sunday.
Mulino was declared winner having secured about 34 per cent of the ballots tallied with 90 per cent of the total vote counted. Ricardo Lombana, who trailed in second place with about 25 per cent of the vote, congratulated Mulino on his victory.
Mulino, a pro-business right-wing politician, faces a daunting task of mending social divisions and regaining the faith of an electorate fed up with political graft.
Among his top priorities will be fixing Panama's pressing economic problems, tackling corruption, and restoring the country's reputation as an investment haven.
"We know that now as president he can fix the country," said Hayde Gonzalez, 46, a medic who danced with her daughters in the centre of the capital upon hearing Mulino was pulling ahead as votes were counted.
"There will be more security and the economy will recover," she added.
Mulino has promised to usher in prosperity through ambitious infrastructure investment and a higher minimum wage, while suggesting he would keep Martinelli out of jail.
Magali Rosa, 60, a retiree, said she voted for Mulino because she felt he could bring more jobs and improve security, and that during the Martinelli there was "a lot of money" for everyone.
Mulino will take office on July 1 for a five-year term.
