Ashton, who mediated the talks, announced conclusion of the talks, saying: "The text has been initialed by both prime ministers," the BBC reported.
Serbia had rejected a proposal earlier this month that Belgrade said did not "guarantee full security and protection of human rights to the Serb people in Kosovo."
Serbia had wanted Serbs living in Kosovo to be able to choose the regional police commander, B92 reported.
Serbian negotiators had said they would not sign an agreement if Kosovars insisted on having a seat at the United Nations.
Friday's agreement reportedly contains 15 points, including the granting of "serious powers" to Serb communities in Kosovo and financing for healthcare, education and spatial planning that is "tied to Serbia."