The Security Council resolution led to Syria's withdrawal after a 29-year presence.
Abbas made no statement to the news media upon his arrival on Friday.
The source said he planned to meet President Emile Lahoud, Parliament Speaker Nabih Berri and interim Prime Minister Najib Miqati to discuss opening a Palestinian embassy in Beirut and improving living conditions for the 400,000 Palestinian refugees in Lebanon.
His visit comes a day after he met with Syrian President Bashar al-Assad and the heads of 10 Palestinian resistance groups in Damascus in an attempt to convince them to join a government of national unity overseeing Israel's August withdrawal from the Gaza Strip.
Islamic Jihad and the Popular Front for the Liberation of Palestine rejected Abbas' offer.
A similar rebuff came earlier in the week from the Palestinian resistance movement, Hamas, which has popular support and is seen as a political rival to Abbas.
Abbas was also to meet with Palestinian group leaders, particularly those from Fatah.
He was accompanied by his spokesman and two high-ranking security officials.
His last visit to Lebanon was in December 2004.