Lebanon and Israel both claim about 860 square kilometres of the Mediterranean Sea that are home to offshore gasfields.
The agreement to demarcate the maritime border would mark a major breakthrough in relations between the two countries, which are technically at war, and offers a potential boost for Lebanon's crisis-hit economy.
Beirut and Tel Aviv must send letters to Washington expressing their approval of the deal mediated by US envoy Amos Hochstein. The US will then issue a notice to both officially announcing the deal is in force.
“This indirect agreement responds to Lebanese demands and maintains all our rights,” Mr Aoun said in a televised speech on Thursday.
“I hope the end of these negotiations is the promising start to placing the cornerstone for the economic growth that Lebanon needs through extracting oil and gas,” he said.
Mr Aoun, whose presidential term ends this month, said the deal would “add stability, security and development that our nation Lebanon needs”.
His announcement came hours after a meeting with caretaker prime minister Najib Mikati and Parliament Speaker Nabih Berri, who had received copies of Mr Hochstein’s latest version of the agreement earlier this week.
Mr Berri had earlier called for MPs to receive a copy of the agreement as well, amid criticism in Beirut that the terms have had insufficient parliamentary oversight.
Members of parliament who spoke to Mr Berri after a session on Thursday told him that as an international treaty, the deal should be voted on in parliament. One of them, MP Melhem Khalaf, said a failure to send the agreement to parliament would be “a constitutional violation”.
US President Joe Biden said on Tuesday Israel and Lebanon had agreed to “formally” end their maritime border dispute, and that their leaders both told him they were ready to take next steps.
Israel’s Cabinet on Wednesday backed the deal by a “large majority” of its ministers. The agreement will be forwarded to the Knesset, or parliament, for a two-week review period before a final Cabinet vote.
Israel also hopes to exploit gas reserves and hopes the deal will reduce the risk of war with Lebanon’s Iran-backed militant group Hezbollah.
The agreement stipulates that the disputed waters would be divided along a line straddling the Qana natural gasfield.
Gas production would be based on the Lebanese side, but Israel would be compensated for gas extracted from its side of the line.
— With reporting from agencies.