Some 5,000 people congregated in a square outside Mr Abbas's government headquarters in the West Bank. Many hoisted Palestinian flags and balloons in the colours of the flag.
Mr Abbas told the crowd that "we now have a state" and that "the world has said loudly, 'yes to the state of Palestine."'
The UN decision to recognise Palestine as a non-member observer state does not change the situation on the ground.
The Palestinians believe the strong endorsement will boost their leverage in future peace talks.