In a decree, Abbas said parliamentary and presidential elections will be held in the besieged Gaza Strip and occupied West Bank on May 22 and July 31, respectively.
They will be the first such votes after 15 years.
Also, elections for the National Council of the Palestine Liberation Organization (PLO), which represents the Palestinian cause internationally, will be held on August 31.
Hamas hailed the decision, saying, “We have worked in the past months to overcome all hurdles to reach this day.”
Back in October, Hamas and Fatah, led by Abbas, agreed on holding Palestinian elections in six months.
The Palestinian leadership has been divided between Fatah and Hamas since 2006 when the latter scored a landslide victory in parliamentary elections in the besieged Gaza Strip.
Hamas has ever since been running the densely-populated coastal enclave, while Fatah has been based in the autonomous parts of the Israeli-occupied West Bank.