Ibrahim Boubacar Keita is to become Mali's new president after his rival conceded defeat in the second-round runoff elections.
Ex-Finance Minister Soumaila Cisse said he had congratulated Keita on winning the vote and wished him good luck, the AFP news agency reported on Monday.
Cisse's concession, hours after he complained the election had been marred by fraud, will deepen optimism for Mali's recovery.
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"The general feeling here is that people are actually happy that this has come to a peaceful end, and that Mali finally has a president," he said.
Keita, a former prime minister, inherits a broken nation and must still negotiate peace with northern rebels.
"This is the symbol of the new Mali. Of a Mali, now confident of its success, following the line that the voters have wished for and have wanted. I believe it is Mali that has won." said Keita on Monday.
No official results
No official results have yet been released following Sunday's runoff but Keita was believed to have won by a wide margin.
Keita swept the July 28 first round with nearly 40 percent of votes on a ticket to restore order after a March 2012 military coup allowed separatist rebels to seize control of the northern two-thirds of Mali.
Cisse said on Monday that the vote had been tainted by intimidation. However, international and local observers said that, despite small irregularities, the process had been credible.
"This election, from a democratic standards point of view, is a success," said the head of the European Union Observer mission, Louis Michel.
"It is an election that allows Mali now to start finishing the process that it has begun: the return to a normal democracy," he added.
French President Francois Hollande said the vote was a victory for democracy and vowed France would "stand by" the west African country.
"What has happened since the French intervention... up to the election of a new Malian president is a success for peace and democracy," Hollande said.
France sent thousands of troops in January to break rebels' grip on northern Mali. It now aims to pull out its contingent to a rapid response team of 1,000 troops to face the scattered threat, while handing broader security duties to a 12,600-strong UN peacekeeping mission being deployed.
The US meanwhile has signalled that it was prepared to resume aid to Mali following the election.