The victory of Pablo Salazar, a senator heading a broad opposition coalition, added further humiliation to the Institutional Revolutionary Party's (PRI) presidential election loss last month.
In addition, Salazar said, his win was a "sign" to the Zapatista rebels to resume peace talks.
"We Chiapans have reaffirmed our identity," a hoarse and exhausted Pablo Salazar told Reuters. "The self-esteem of a people who have wept so much has been lifted. Yesterday (Sunday) we cried with joy."
With 96.5 percent of Sunday's ballot counted, Salazar had 52.71 percent of the vote, compared to 46.89 percent for Sen. Sami David of the PRI, the state Electoral Board said. About 50 percent of the 2 million Chiapas voters cast ballots.
David, in a news conference Monday evening, conceded defeat, saying he acknowledged the desire for change "that motivated people to vote in a majority for Pablo Salazar."
"I'm sure he will be up to the democratic challenge that Chiapas society today presented to him," he added.
The victory by Salazar, who headed an eight-party coalition spanning the left-leaning to the right-of-center, was widely expected to breathe new life into stalled peace talks between the government and Zapatista rebels.
The armed group catapulted to international attention six years ago, emerging from the jungle of the southern state to lead a fight for indigenous rights.
Chiapas, Mexico's most impoverished state, is home to deeply rooted pre-Columbian Mayan Indian culture and traditions.
The Chiapas result mirrored Mexico's July 2 general elections, in which opposition candidate Vicente Fox toppled PRI candidate Francisco Labastida, the party's first presidential defeat in 71 years of rule.
Fox, of the conservative National Action Party (PAN), sent an early message of congratulations to Salazar Sunday and said he would support him in bringing peace to Chiapas.
The president-elect said the vote "confirms the will of the citizens to push changes that Mexico needs for democracy, legality and peace."
Salazar's campaign hinged on bringing an end to the conflict and he vowed to mediate a new round of talks between the federal government and the Zapatistas.
Salazar, a lawyer, said Chiapas was in dire need of social and political reconstruction, although he was quick to add that any reconciliation of the conflict would not mean impunity from criminal prosecution.
He said in a radio interview that massacres such as the one that occurred at Acteal, a highlands area near San Cristobal, when armed civilian bands linked to the PRI killed 45 Tzotzil Indians in 1997, would not go unpunished.
"Acteal is a wound, an act of brutality, that cannot remain in impunity," sad Salazar.
Chiapans streamed into the streets Sunday to celebrate a change in their state's leadership soon after early results gave Salazar a decisive lead.
"This will bring change in every sense," said a joyful Esperanza Garcia as she waited to greet the victor.
Until recently, alleged coercion, corruption, vote-buying as well as tradition made PRI victories seem inevitable in all elections in Chiapas and elsewhere in southern Mexico.