King Salman received the prime minister and his accompanying delegation at the king's palace, the Saudi Press Agency (SPA) said.
Abadi is to take part in a meeting on Sunday to establish a joint Saudi-Iraqi coordination council aimed at boosting cooperation.
US State Secretary Rex Tillerson, who arrived also on Saturday, is to take part in the meeting, officials said.
Abadi's visit to Saudi Arabia is the second this year since Saudi Foreign Minister Adel Al-Jubeir visited Baghdad in February, the first such visit by a top Saudi official since 1991.
After former dictator Saddam Hussein’s August 1990 invasion of Kuwait, Riyadh severed relations with Baghdad and closed its border posts with its northern neighbor.
Ties remained strained even after Saddam’s ouster in the 2003 US-led invasion of Iraq, since when successive Shiite-dominated governments in Baghdad have stayed close to Tehran.
Iraq is seeking economic benefits from closer ties with Saudi Arabia as both countries suffer from a protracted oil slump. Saudi Arabia is also seeking to counter Iranian influence in Iraq.
Abadi's visit coincides with Saudi Energy Minister Khaled Al-Falih’s high profile visit to Baghdad where he called for the strengthening of economic relations to boost oil prices.