The energy, water and resources minister told Israel Radio the agreement would be signed Monday in Washington.
"We are talking about a historic process, a dream come true , the result of significant and strategic cooperation between Israel, Jordan and the Palestinian Authority," Shalom, who was in Washington, told the Hebrew daily Yedioth Ahronoth.
The 180-kilometer (112 mile) Red Sea-Dead Sea conduit, also known as the Two Seas Canal, will carry water north and slow down the desiccation of the Dead Sea, the Hebrew daily said..
Israelis, Palestinians and Jordanians will profit from the agreement, the report said.
Under the agreement, about 200 million cubic meters of water will be pumped from the Red Sea each year. A water purification plant to be erected in Aqaba, Jordan, will purify water to be shared by Israel, Jordan and the Palestinians, the newspaper said.
The first pipeline will be laid in Jordan.
The cost of the project, expected to take five years to complete, is estimated at up to $400 million.