Colombian President Juan Manuel Santos announced the new deal in a TV address Saturday evening, saying it will build a "broader, deeper peace."
A peace deal negotiated earlier this year with FARC rebels was unexpectedly defeated by Colombian voters
in October. Many were angered by what they saw as insufficient punishment for those who perpetrated a litany of crimes against their people.
Negotiations for a peace deal continued after the defeat with rebels and those opposed to the original agreement.
Among the new stipulations are reparations for victims which will come from FARC's assets and money, Santos said.
FARC can still form a political party under the agreement and members with minor offenses can apply to get their records cleared.
One of the chief negotiators of the FARC guerrilla movement, Ivan Marquez, tweeted, "The new peace accord is the victory for Colombia."
The accord also sets up transitional areas where FARC members stay to be rehabilitated and have "activities of reparation," Santos said.
Santos was awarded the Nobel Peace Prize
this year for "his resolute efforts" to end the country's civil war.
Praise from U.S. diplomats
US Secretary of State John Kerry issued a statement saying, "I want to congratulate the government and people of Colombia on achieving a revised peace agreement."
"President Santos and his negotiating team, those from the 'No' campaign, and other important sectors of Colombian society deserve credit for engaging in a far-reaching and respectful national dialogue following the plebiscite," Kerry said.
He said the United States will "support full implementation of the final peace agreement."
US National Security Adviser Susan Rice congratulated the government of Colombia for reaching the deal.
"We appreciate how difficult and complicated the negotiations have been and recognize that the new provisions, while an important step forward, will not necessarily satisfy everyone," she said in a statement.