Sudan President Omar al-Bashir has lifted a state of emergency imposed in 1999, but it will remain in force in Darfur and two eastern states.
Mr Garang (left) is now the second most powerful man in Sudan
The announcement follows the swearing in of former southern rebel leader, John Garang as first vice president.
Former prime minister and opposition leader Sadiq al-Mahdi has condemned the country's new constitution.
He says it is a bilateral deal between Mr Garang's Sudan People's Liberation Movement and the ruling party.
Other opposition parties were under-represented, he argued.
The constitution, brokered as part of a recent peace deal which ended a long civil war, came into force on Saturday.
"We think it is a deficient draft and a deficient constitution," Mr Mahdi said.
"There are many problems now in the east, in the west and in other parts of the Sudan whose resolution will require them to be represented in a comprehensive agreement and be represented in the constitution."
Fighting continues in the western region of Darfur, while rebels in the east have resumed fighting in recent weeks.
Under the new constitution, 52% of government and parliament posts will be held by the ruling National Congress, while former rebel leader John Garang's SPLM has been given 28% of power.
Northern and southern opposition parties share the remaining 20%.
Mahdi says minor opposition parties are under-represented
Mr Mahdi acknowledged the constitution was "a step forward", but warned that the current agreement would lead to a "diarchy" - a country headed by two leaders.
He called on all those who had been left out to unite in a national front which would monitor "oppression and corruption" in the country.
Mr Garang was sworn in as Sudan's vice-president on Saturday after the signing of the new charter during a ceremony in Khartoum.
Under the peace deal, Sudan's new oil wealth will be shared between north and south, Islamic Sharia law will not be applied in the south and the south will hold a referendum on secession in six years' time.
The conflict between the predominantly Muslim north and Christian south, which lasted more than two decades, claimed 1.5m lives.