Thursday's ceremony, attended by Sudan's President Omar al-Bashir and second vice president Osman Ali Taha, opened with Muslim and Christian prayers at Khartoum's Republican Palace.
Posters of Kiir and his former archfoe, President Omar al-Bashir, were on display in the capital while security has been stepped up to guard against the kind of deadly rioting that rocked the streets after Garang's death.
Kiir has vowed to uphold peace in line with an agreement signed in January that ended a two-decade conflict between north and south, Africa's longest running war in which about two million people had died.
The peace process was interrupted by the death of Garang in a helicopter crash on 30 July, just three weeks after the former southern rebel leader had taken office as vice president under the January accord.
"Despite the fact that we have lost our hero, the man who brought peace, Dr Garang, we will continue with the same vision, with the same objective, and we will implement the Comprehensive Peace Agreement," Kiir said on Wednesday.
He spoke in Arabic, the language of northern Sudanese, in a bid to shore up his credentials as a national leader, while English is widely spoken in the animist and Christian south.
One of the primary challenges for Kiir, the ex-southern rebel military chief, will be to form a national unity government with Bashir.
"Despite the fact that we have lost our hero, the man who brought peace, Dr Garang, we will continue with the same vision, with the same objective, and we will implement the Comprehensive Peace Agreement"
Salva Kiir, Sudan vice president
Kiir, who replaced Garang as head of the Sudan People Liberation's Movement/Army (SPLM/A), will have to help solve disputes about oil-rich areas on the north-south border.
He is also to continue talks with several Khartoum-backed southern militia chiefs with a view to rallying them to the peace agreement.
Kiir has pledged to continue in Garang's footsteps and carry on his dream for a democratic and prosperous Sudan, which does not discriminate against citizens on the basis of race, creed, gender or ethnicity.