"The State of Sudan is an embracing homeland, wherein races and cultures coalesce and religions conciliate," reads the first sentence of the document.
While stating that the majority of Sudanese are Muslims, it notes that "Christianity and customary creeds have considerable followers."
Although Islamic law remains the basis of the law, the new constitution says it won't be applied in the mainly Christian and animist south, and removes a requirement that the president be Muslim.
"This is a call for tolerance and for siding with the people, with the man in the street," Vice President Ali Osman Mohammed Taha told lawmakers after the vote. "We have passed a constitution ending 50 years of civil war that produced grudges, produced tragedies, produced widows and orphans and retarded our economy and fanned hatred."
He said the constitution would help overcome the past - Sudan has faced civil wars for most of the years since it gained independence from Egypt and the U.K. in 1956 - and give the government a chance to focus on improving the living conditions of its people.
"We want to lead the war against poverty, provide better services and spread education," Taha said. "We want to go out to the world give it our best and take the best the world has to offer."
The new charter follows a January peace agreement between the government and southern rebels who had fought a two-decade war for more autonomy.
The rebel leader, John Garang, will be sworn in as the country's top vice president on Saturday, ushering in a government of national unity that will take office in August.
It will be the first time a Christian is appointed as first vice president, a position second only to the president. Taha will remain as a vice president.
In another first, the constitution also allows women as well as men to pass on Sudanese nationality to their children. The new constitution 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.
Although the southern civil war was fueled by historical disputes and competition for oil and other resources, religion played a large role and was an issue during peace talks.
The talks stalled once over rebel insistences that the capital, Khartoum, should not fall under Islamic law. The rebels eventually yielded on that point, with the understanding that non-Muslims would not be harassed - as they have been in the past - in Khartoum.
The government, weary of international political and economic isolation, had begun to move away from Islamic law even before the January peace deal that paved the way for the constitution.
The new charter has been criticized by some, notably influential opposition leader Hasan Turabi, who said it should have been put to the people in a national referendum rather than being decided by the 330-member National Assembly.