President Clinton made the announcement Wednesday after Albright held separate talks with the leaders of Israel and Syria.
Israeli Prime Minister Ehud Barak will hold a day or two of initial talks next week with Syrian Foreign Minister Farouk al-Sharaa, Clinton said at the start of a news conference Wednesday.
After that, intensive negotiations will be held at a yet-to-be determined location, Clinton added.
The "Israelis and Syrians still need to make courageous decisions in order to reach a just and lasting peace, but today's step is a significant breakthrough, for it will allow them to deal with each other face to face and that is the only way to get there," Clinton said.
While Clinton said the talks would be "resumed from the point where they left off," he would not give details about where that point is.
Syria has long maintained that the talks, which were suspended in March 1996, left off with the late Israeli Prime Minister Yitzhak Rabin making a commitment to return all of the Golan Heights in exchange for peace with Syria.
However, Israel maintains that the offer was "hypothetical" to see if Syria was willing to meet Israeli demands on security and normalization.
Asked what concessions both sides made to resume the talks, Clinton would not say.
"I think it's very important at this point that we maximize the chances for success, which means it would not be useful for me to get into the details," he said. "But the negotiations are resuming on the basis of all previous negotiations between Syria and Israel, and with the United States."
Israel's ambassador to the United States, Zalman Shoval, speculated on CNN International that "maybe, maybe there has been a change" in some of Syria's hard-line demands.
Shoval also expressed disappointment that Syrian President Hafez Assad will not participate in the talks.
Clinton said at the news conference that although Assad will not be in Washington next week, he "is very personally involved."
Clinton also said he hoped the resumption of Israeli-Syrian talks would lead to negotiations between Israel and Lebanon.
Clinton also said he had no illusions that negotiations will be easy.
"On all tracks the road ahead will be arduous," he said. "Success is not inevitable. Israelis, Palestinians, Syrians and Lebanese will have to confront fateful questions.
"But let there also be no misunderstanding: We have a truly historic opportunity now. With a comprehensive peace, Israel will live in a safe, secure and recognized border for the first time in its history."
During her Middle East shuttle this week, Albright had her sights fixed on two negotiating tracks.
On the one hand, she wanted to breathe life into the Israeli-Syrian negotiations; on the other, she sought to keep Israeli-Palestinian talks from faltering.
Albright was optimistic about Israeli-Syrian prospects after holding separate talks with the leaders of both countries, but she did not elaborate.
Albright arrived in Israel from Syria, where she met with Syrian President Hafez Assad for nearly three hours Tuesday.
For his part, Barak said Wednesday that Israel was aware a peace accord with Syria would require "painful compromises."
At the same time, he said, "I will not sign any agreement that will not, to the best of my judgment, strengthen Israel rather than weaken it."
Albright, who was in the region on a four-day mission, also welcomed Barak's announcement that Israel would not issue new construction permits for Jewish settlements while Israel and the Palestinians try to reach a framework for a final peace treaty.
Each side needs to avoid taking steps that "embarrass the other and make negotiations more difficult,'' Albright said.
On the eve of Albright's visit, the chief Palestinian negotiator in the final-status talks, Yasser Abed Rabbo, said there would be no progress in the discussions unless Israel stops expanding Jewish settlements in the West Bank and Gaza Strip.
Barak made the announcement in an effort to defuse the crisis, but on Wednesday a spokesman for Palestinian Authority President Yasser Arafat rejected the offer.
Settlement leaders and right-wing coalition members were likewise unimpressed with Barak's announcement.
Housing Minister Yitzhak Levy, a member of the National Religious Party, said he would meet with Barak to determine whether the decision was made for the purpose of negotiations or represented a long-term government policy.
Based on those discussions, Levy said, the National Religious Party would consider whether it would remain in the governing coalition.
In addition to the settlement issue, Israel and the Palestinian Authority remain deadlocked over an Israeli withdrawal from an additional 5 percent of the West Bank, a move that was to take place last month.
The Palestinians have stated that they want a say in which lands will be turned over. Israeli officials just as steadfastly maintain that the decision is theirs alone to make.
The two sides failed to overcome their dispute in discussions this week with U.S. Middle East peace envoy Dennis Ross, who arrived in the region over the weekend to prepare for Albright's arrival.
Albright also met Wednesday with Foreign Minister David Levy to discuss efforts to include Israel in the U.N.'s Western European and Others Group. Israel is the only U.N. member excluded from such a group, which is a prerequisite for participation in important committees, including the Security Council.
(JTA correspondent Naomi Segal in Jerusalem contributed to this report.)