The agency said shares in the 100,000 barrels per day refinery, located near Alexandria, had been bought by a "Libyan government body," but giving no other identity details of the new 39 percent stake holder.
The deal was struck in the Egyptian stock market on Monday, with Tripoli buying over a third of the shares held in MIDOR by the state-owned National Bank of Egypt (NBE).
NBE in 2001 raised its initial 13 percent stake in the refinery to 39 percent, by buying the 20 percent holding of Israel's Merhav group and six percent held by other companies that have Israeli connections.
The state-owned Egyptian General Petroleum Corporation (EGPC) continues to have a controlling stake in MIDOR, as it owns directly 40 percent of the shares and another 20 percent through its subsidiaries Petrojet and ENPPI.
The other one percent is held by the state-owned Suez Canal Bank.
The 1.2 billion-dollar MIDOR was planned in the late 1990s as one of the most advanced refineries in the Middle East, and was the biggest Arab-Israeli joint venture since Egypt signed a peace treaty with Israel in 1979.
Merhav, which initially held 40 percent of the refinery's capital, began pulling out in 2000, as Egyptian-Israeli relations soured after the breakout of the latest Palestinian uprising to occupation.
Most of MIDOR's products go to the Egyptian market and the rest are exported to other Mediterranean countries.
The deal with Libya comes as Cairo and Tripoli agreed last year to set up a twin pipeline to carry Libyan crude to Alexandria and Egyptian gas to Libya for export.
Egyptian officials said the oil pipeline would carry 150,000 bpd of Libyan crude to be refined in Egypt for domestic consumption and exports.