Al-Bashir was re-sworn in as president on Saturday with a pledge to uphold and respect the new charter.
Shortly after the signing, Garang took the oath of office as first vice-president, a historic move that many see as the first real evidence of a peace deal signed earlier this year.
Garang, who returned to Khartoum a day earlier, for the first time in 22 years, will be second in command only to the president.
He will be the first southerner and Christian to hold such a high position in the largely Muslim government.
Garang and al-Bashir also signed an interim constitution that for the first time lays down freedoms of religion and expression as human rights.
The new charter also finally brings to an end the state of emergency, in force on and off since al-Bashir seized power in a 1989 coup that saw all political parties outlawed.
Sudan's former first deputy president Ali Uthman Taha will be sworn in as the country's second deputy president, reports Aljazeera's correspondent in Khartoum, Muhammad Fal.
Garang (L) received a warm
welcome from al-Bashir (R)
A number of foreign dignitaries, including UN Secretary-General Kofi Annan, US Undersecretary of State Robert Zoellick and South African President Thabo Mbeki attended the ceremony.
"For the first time in many years, a lasting peace for all the people of Sudan is now within reach. To secure that peace, no effort must be spared," Annan told the gathering.
"This is a great day. A new Sudan is being created which gives us a lot of hope for the future and for the Sudanese,"
added Amr Moussa of the Arab League.
Saturday was declared a public holiday because of the events.
Garang's appointment is part of a January peace deal to share power and wealth with long-marginalised southerners.
Al-Bashir, late on Friday, dissolved the Council for the Southern Provinces, a move that was meant to pave way for Garang to form the southern transitional government, Aljazeera correspondent said.
Garang, who arrived triumphantly in the capital on Friday for the first time since the civil war began in 1983, was welcomed by al-Bashir and later by hundreds of thousands of ecstatic Sudanese at a rally in northern Khartoum's Green Square.
The 60-year-old founder of the Sudan People's Liberation Army was central to the southerners' fight for autonomy and greater rights against Khartoum governments that sought to impose Islamic law throughout Africa's largest nation.
"For the first time in many years, a lasting peace for all the people of Sudan is now within reach. To secure that peace, no effort must be spared"
Some two million people have died from fighting, famine or disease as a result of the war, which began in 1983.
Although Islamic law remains the basis of governnance, the constitution says it will not be applied in the south, and removes a requirement that the president should be a Muslim.
In another first, the constitution also allows women, as well as men, to pass on Sudanese nationality to their children.
It provides for a coalition government, wealth and power sharing and democratic elections within three years. The south will also have a referendum on secession after six years.
The peace deal gives al-Bashir's party 52% of government and parliament and the Southern People's Liberation Movement (SPLM) 28%, with northern and southern opposition groups taking the remaining 20%.
It also shares oil wealth roughly equally between the north and the south, where the main oil fields lie.
Over two million people have
been displaced by Darfur conflict
But the southern peace deal does not cover a separate conflict in Sudan's western Darfur region, which has been raging for more than two years. Tens of thousands of people have been killed and more than two million have fled their homes.
A smaller revolt has recently expanded to the east of Sudan, Africa's largest country.
Annan told Garang and al-Bashir that it was important to reach a settlement for Darfur and begin talks in the east, as well.
"The peace process between north and south must be made irreversible - which it will not be unless it takes root in the East and in the West, as well," he said. "As an immediate priority, therefore, the government... must work to resolve the conflicts in Darfur and in eastern Sudan."