Kiir replaced John Garang, who died in a helicopter crash on 30 July near the Uganda-Sudan border.
"Despite the fact that we have lost our hero, the man who brought peace, Dr John Garang, we will continue with the same vision and objectives, and will implement the Comprehensive Peace Agreement [CPA]," Kiir said at the ceremony. "The agreement provides the last chance for Sudan's unity."
Sudanese President Umar al-Bashir congratulated Kiir and hailed the SPLM/A for making a "courageous, historic" decision to name him their new chairman.
"Our country enters a new stage today as we all witness the swearing in of Salva Kiir Mayardit, the successor of the hero of peace, Dr John Garang De Mabior," Bashir said.
"The government of Sudan will present the results of the investigation of the death of Dr John Garang to all Sudanese people and the international community with transparency," he added.
Kiir arrived in Khartoum on Wednesday and was welcomed by Sudan's Second Vice President, Ali Uthman Mohamed Taha and various SPLM/A officials.
"I am delighted to be speaking to you here in Khartoum International Airport - my first visit in 22 years," Kiir told reporters upon arrival.
"I am appealing to all the people of Sudan, and the people from southern Sudan in particular, to remain calm and not to repeat what has happened a few days ago," he added, referring to the violent riots that erupted around the country on 1 August and left at least 130 people dead.
Garang, who had led the former rebel SPLM/A through 21 years of civil war against the Sudanese government, had been sworn in as First Vice President of Sudan on 9 July, in accordance with the CPA.
He died en-route to southern Sudan from Uganda, following a meeting with Ugandan President Yoweri Museveni. All the people travelling with him died when the helicopter came down near the Uganda-Sudan border.
The governments of Sudan and Uganda have both set up panels to investigate the crash. Garang was buried in the southern town of Juba on 6 August.
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