The appointment on Friday came a day after the sacking of three security chiefs for failing to stop rocket and mortar attacks on Jewish settlements, a Palestinian official said.
The deputy police chief, Mahmud Asfur, was provisionally promoted to the top job to replace General Saib al-Ajiz, the official said.
Also sacked on Thursday were the head of national security, General Abd al-Razzak al-Majaida, and the national security chief in southern Gaza, General Umar Ashur.
Abbas was said to be furious after members of the resistance movement Hamas were able to fire more than 30 mortar rounds and rockets at Jewish settlements on Thursday, prompting Israel to cancel a top-level meeting to discuss implementation of agreements reached at Tuesday's peace summit in Egypt.
Hamas' military wing, the Izz al-Din al-Qassam Brigades, said the attacks were in "response to the Zionist crimes which are continuing and have cost the lives of Fathi Abu Jazar and Hasan al-Alami".
Al-Alami was killed in an explosion near his home on Wednesday, while Abu Jazar died after being shot on Wednesday in Rafah.