The United States and Israel signed an agreement yesterday that will eliminate all trade barriers between them within 10 years, a move that President Reagan hailed as adding "a new dimension to the special relationship between our countries."

After they signed the agreement here, U.S. Trade Representative William E. Brock and Israeli Trade Minister Ariel Sharon toasted each other with kosher champagne from California and Israel.

"Our two countries are bound to benefit from this agreement," said Sharon. He called it "an additional milestone in U.S.-Israeli relations" and said it will "foster greater unity and friendship between our two nations."

Brock predicted that the current $3.5 billion in two-way trade between the United States and Israel will quadruple within three years as a result of the agreement, which already has been approved by the Israeli Cabinet and the Knesset (parliament). Congress has 60 days to approve or vote down the agreement once it is submitted by the president, probably later this week.

The signing ceremony was held during the annual meeting of the major pro-Israel lobbying group in the United States, the American Israel Public Affairs Committee (AIPAC), which has been working hard to make sure the agreement wins congressional approval.

The free-trade pact was one of a number of military and economic concessions made by President Reagan during his November 1983 meeting with Yitzhak Shamir, Israel's prime minister at that time, in an effort to help the sagging Israeli economy and strength strategic ties between the two nations.

Under the agreement, areas of the two countries' economies that are considered especially sensitive to imports will escape the immediate effects of duty-free status, but within 10 years they will have been phased in. Some U.S. industries feared they could be hurt by duty-free imports from Israel.

President Reagan said the agreement gives "unprecedented recognition" to the increasingly important areas of trade in services and investment -- a prime goal of U.S. trade policy with other nations. The president said he hopes the agreement with Israel will stimulate liberalization of the world trading system.