BOGOTÁ, Colombia—Peace talks between the Colombian government and Marxist rebels have concluded successfully, the two sides said Wednesday night, after nearly four years of contentious discussions to end a half century of conflict that has cost more than 200,000 lives.

“We have reached a final accord, complete and definitive, to end an armed conflict with the FARC,” President Juan Manuel Santos said in a televised speech, referring to the Revolutionary Armed Forces of Colombia, which took up arms against the Colombian state...