Bechara al-Rahi is expected to meet Hariri, who stepped down during a televised address on November 4 from Riyadh, where he is rumoured to be under de facto house arrest, despite his insistence that he was "free".
He is also set to meet King Salman and Crown Prince Mohammed bin Salman in a trip that symbolises a rare inter-religious exchange in the ultra-conservative kingdom, which is home to the holiest sights in Islam.
"Patriarch Bechara al-Rahi's... visit stresses the kingdom's approach for peaceful coexistence, closeness and openness for all sections of Arabic people," Saudi Gulf affairs minister Thamer al-Sabhan said on Twitter.
Upon his arrival, the patriarch met with members of the Lebanese community.
"We will maintain a strong friendship between Saudi Arabia and Lebanon," he said.
"This is our history even if we have had stormy relations sometimes. (There) is a history of friendship with this dear kingdom."
Hariri's resignation, which has thrown Lebanon into crisis, came against the backdrop of mounting tensions between Sunni Saudi Arabia and Shiite Iran, which back opposing sides in power struggles in hotspots such as Syria and Yemen.
French Foreign Minister Jean-Yves Le Drian has said France was "worried by the situation in Lebanon" and wanted to see the government there "stabilise as quickly as possible".
He is set to visit the Saudi capital on Thursday.
France joined Germany and the European Union on Monday in calling for an end to external interference in Lebanon -- buffeted for decades by conflicts between bigger players in the region such as Iran and Syria.