Haniyeh’s visit coincides with an official visit by Palestinian President Mahmoud Abbas, who arrived in the kingdom on Monday.
The two Middle East powerhouses had held several rounds of dialogue in Iraq and Oman before reaching the agreement to mend ties on March 10 in China.
The visit will be the first by Hamas to Saudi Arabia in years.
Recent diplomatic rapprochement between Riyadh and Tehran has paved the way for the swap of nearly 900 detainees held by rival forces in war-torn Yemen.
More than 300 prisoners scheduled to fly between Sanaa and Aden on Friday, while detainees will also be released in Marib and Mokha, as well as in Riyadh and Abha in neighbouring Saudi Arabia.
Diplomats say Damascus' return to Arab League and presence at an expected summit in May will be discussed in Friday's meeting of regional powers, but Qatar's premier says nothing has been proposed.
Saudi state news agency says both foreign ministers spoke by phone for the second time in a few days.
Chinese President Xi Jinping’s three-day official trip could have a significant bearing on Washington and Riyadh’s strained ties.
Decision of OPEC+ to cut its oil production target by two million barrels per day was "purely economic" and adopted through consensus, says Saudi Foreign Ministry, after Washington vowed "consequences" for US-Saudi ties.
Once traditional allies of the US in the Middle East are now turning their backs on Washington and cozying up to Moscow and Beijing in a significant shift of loyalties.
Iraqi Prime Minister Mustafa al Kadhimi arrives in Iran's capital after a visit to Saudi Arabia to resume talks between the two countries with the aim of "boosting security and stability in the region".
Tehran and Riyadh severed diplomatic relations in January 2016 following an attack on the Saudi Embassy in Tehran after Shia cleric Nimr al Nimr was executed by Saudi authorities.
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