Salahuddin Rabbani will chair the country’s High Peace Council, which leads Afghan efforts to negotiate with the Taliban.
Mr Rabbani is currently ambassador to Turkey. His father, a former president and mujahideen leader, was killed by a suicide bomber last September.
His death was seen as a major blow to reconciliation efforts in the country.
Mr Rabbani was killed by a bomb hidden in the turban of a suicide attacker posing as a Taliban envoy.
The Taliban denied sanctioning the killing, which took place during a meeting at the former president’s house in Kabul. Pakistan also denied suggestions it had any role in the attack.
Correspondents believe the attacker was among those Taliban members opposed to the talks initiative.
Salahuddin Rabbani is US educated and worked for the Afghan mission at the United Nations in New York before taking up his post as ambassador in Istanbul.
A presidential statement said he had been elected by a majority of High Peace Council members. His appointment was aimed at “consolidating national unity and preventing foreign interference”, the statement said.
Mr Rabbani takes over after seven months during which the 70-member council has had no leader.
His task is complicated by the fact that the Taliban view the Western-backed government of Hamid Karzai as illegitimate.
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