Rabbani replaces his father, the former President Burhanuddin Rabbani who was assassinated in September last year by a suicide attack by a bomber carrying a bomb hidden in a turban.
His death was a major setback to reconciliation efforts with the Afghan Taliban and exploratory moves toward peace talks.
A statement from the president's office confirmed the appointment of Rabbani.
“Salahuddin Rabbani was elected the head of High Peace Council by majority of High Peace Council members in a meeting today,” the statement said.
“For the sake of national unity, and to stop the foreign interferences, [the] Afghan president called his appointment useful."
Salahuddin, born in 1971, is currently Afghanistan's ambassador to Turkey. His appointment as Kabul's chief peace negotiator with the Taliban ends a seven-month gap at the top of the 70-member council.
"The presence of foreign troops has prolonged conflict and insecurity," he said in a statement issued by President Hamid
Karzai's office, aimed at mollifying those who are demanding the withdrawal of all foreign forces from the country.
"We will have achievement in the peace process when the leadership is in the hands of Afghans. Without it we cannot move it forward and get the nation's confidence," said Salahuddin.
His father Burhanuddin, an ethnic Tajik, was a celebrated former Afghan leader who fought against the Soviet occupation of the country during the 1980s.
His Jamiat-e-Islami fighters were among the first to reach Kabul after the Soviet exodus in 1989, paving the way for him to become president until his ousting by the Taliban in 1996.
Burhanuddin's murder revealed that the bomber was Pakistani and the assassination had been plotted in Pakistan.
Islamabad angrily rejected the allegation.
Kamdesh raid
Also on Saturday, Afghan forces with air support from NATO combed through the country's mountainous northeast in their third day Saturday of a major offensive against militants in a province that serves as an insurgent supply route from Pakistan.
Mohammad Zareen, a spokesman for Nuristan province, said nearly 30 insurgents have been killed and at least 30 have been wounded in the operation that began Thursday night in Kamdesh district.
Afghan officials say that one policeman and a woman have been killed in the fighting, with another four Afghan soldiers and another woman wounded.
A unit of an unknown number of Afghan commandos and about 400 Afghan policemen are conducting the operation, and another 200 police are soon to join them.
In a statement released on Saturday, the Afghan Defence Ministry said it launched the operation because residents were complaining that insurgents were becoming more active in the area.