Mulino said he had received the electoral result with “responsibility and humility”.
The vote, he told joyous supporters gathered at a hotel in the capital, represented “the majority will of the Panamanian people”.
Runner up Ricardo Lombana conceded defeat moments before the official result was announced.
There were lines at many polling stations as voters in the Central American nation of 4.4 million people cast their ballots for a new president, parliament and local governments.
Opinion polls had shown right-wing lawyer Mulino far ahead of the pack of eight candidates.
But he was made to wait for a last-minute court decision Friday that finally validated his run for a five-year term.
Mulino replaced former president Ricardo Martinelli as the candidate for the right-wing Realising Goals (RM) party after Martinelli lost an appeal against a money-laundering conviction.
The candidacy of Mulino, who had been Martinelli’s vice-presidential running mate until the ex-leader’s disqualification, was then challenged on the basis that he had not won a primary vote or picked his own running mate, as required by law.
The Supreme Court dismissed that complaint Friday in a ruling welcomed by Martinelli, who most Panamanians believe will wield control from behind the scenes, according to a recent poll.
However, after his victory, Mulino vowed he “is not the puppet of anyone”.
Martinelli, who remains popular in Panama, has taken asylum at the Nicaraguan embassy, from where he campaigned for his protégé.
After voting, Mulino went to see Martinelli at the embassy and the two hugged, saying “Brother!” and “We are going to win!” according to a video released by Martinelli.
Many people in Panama long for the days of economic prosperity under Martinelli’s government from 2009 to 2014, aided by an infrastructure boom that included the enlargement of the canal and construction of Central America’s first metro line.
Polls showed voters’ main concerns were the high cost of living, access to drinking water and crime.
The main candidates for president had made pledges to create jobs, stimulate the economy and enact reforms to fight corruption.
“Panama must change. There is too much corruption,” said one voter, 50-year-old teacher Jennifer Navarro.
Mulino, who had served as Martinelli’s public safety minister, has dismissed the criminal case against his former boss as politically motivated, and will now have the power to pardon him.
President Laurentino Cortizo of the majority PRD centre-left party will vacate his seat after a term marred by allegations of widespread official corruption, declining foreign investment and high public debt.
Panama’s presidency has a one-term limit.
About 45 per cent of jobs in Panama today are in the informal market, with unemployment nearing 10 per cent and high income inequality.
The country’s GDP growth is forecast to slow from 7.3 per cent in 2023 to 2.5 per cent this year, according to the International Monetary Fund.
Part of the reason is the Panama Canal, which moves about six per cent of the world’s maritime trade, has limited traffic amid a crippling drought.
Another headache awaiting Mulino is the Darién Gap between Colombia and Panama, through which more than half a million undocumented migrants passed last year – while subjected to abuses criticised by rights groups.
Three million Panamanians were eligible to vote, and more than three-quarters turned out, according to the election tribunal.