"I will lead a high-level delegation to Iran next week to sign an agreement for supplying Kuwait with fresh water from Iran," Shaikh Ahmad Fahd al-Sabah said, quoted by the KUNA news agency on Tuesday.
KUNA said the visit would take place on Saturday.
The two countries signed a memorandum of understanding on the issue in January during a visit by Kuwait's prime minister, Shaikh Sabah al-Ahmad al-Sabah, who was then the foreign minister.
According to the agreement, Kuwait will get 900 million litres of water daily, Shaikh Ahmad said, without providing the financial details of the agreement.
Earlier reports have said the project foresees building a pipeline to channel water from the Karun and Karkheh rivers in southwestern Iran to Kuwait at a cost of $2 billion.
The Kuwaiti minister said the project is "vital" for Kuwait and is classified as "one of the highly important strategic projects."
Negotiations between Tehran and Kuwait City on the project began more than two years ago, when former Iraqi President Saddam Hussein was still in power.
According to initial plans, the pipeline will extend 330km across Iranian territory and then via a 210km pipeline under the Gulf to Kuwait, thus avoiding Iraqi territory.
Kuwait depends almost entirely on sea water desalination for its fresh water requirements which is sold to consumers at heavily subsidised prices. The oil-rich emirate produces around 1.3 billion litres of desalinated water daily and consumes almost all of it.
The two countries are also locked in negotiations for exporting natural gas to Kuwait after signing a memorandum of understanding in January.