Speaking in Jordan, Kerry said Palestinian negotiator Saeb Erakat and Israeli negotiator Tzipi Livni would meet him in Washington "to begin initial talks within the next week or so," Britain's The Telegraph newspaper reported.
"We have reached an agreement that establishes a basis for resuming direct final status negotiations between the Palestinians and the Israelis," he said.
Kerry said details of the agreement were in the process of being formalized, the newspaper reported.
The announcement came after Kerry traveled to Ramallah in the West Bank Friday to meet with Palestinian Authority President Mahmoud Abbas about resuming peace talks.
Abbas has been reluctant to resume negotiations, saying the conditions were too favorable for Israel.
Top Palestinian leaders met Thursday to discuss a proposal from Kerry to resume U.S.-brokered talks with Israel. While terms were not disclosed, Palestinians said it did not include the guarantees needed to resume negotiating, The Washington Post reported.
Kerry extended his Middle East trip in hopes of easing Palestinian concerns. The United States also called on Israeli Prime Minister Binyamin Netanyahu to be more flexible.
Leaders of the Palestine Liberation Organization and others met in Ramallah Thursday with Abbas to consider Kerry's latest outlines but could not reach consensus, the Post said.
Palestinian officials have insisted talks about the future state of Palestine be based on pre-1967 borders. Netanyahu has said Israel was willing to return to the negotiating table immediately but without preconditions.
"A negotiation in which you first say what you are willing to give up is not the kind of negotiation that leads to good results in the Middle East," Deputy Foreign Minister Zev Elkin told Israel Radio Friday.
Also Thursday, President Barack Obama spoke with Netanyahu, encouraging him to keep working with Kerry to resume negotiations with the Palestinians, a White House readout of the conversation said.
"The leaders affirmed the importance of continued close coordination between the United States and Israel on a range of security issues," the readout said.
European Union officials issued directives Friday forbidding use of EU funds for Israeli settlements, The Telegraph said. Israel has said such a policy would harm prospects for peace by predetermining borders, but the EU said international law does not recognize the settlements as sovereign Israeli territory.