Kebbi State Governor Adamu Aliero told a ceremony in the state capital, Birnin Kebbi, that the Islamic law code known as the Sharia would come into immediate effect.
The introduction of the code is very popular with most Muslims but fiercely opposed by Christians who form a minority of the population in northern Nigeria but make up the majority population in the south.
Islam has been a part of life in the north for centuries and since the time of British colonial rule, Islamic or Sharia courts have operated dealing with family and religious matters.
Muslims see the implementation of the full code as an essential part of Islam.
Christians contend that the restoration of powers to Islamic courts to try and to punish people on criminal matters is a violation of the country's constitution.
Obasanjo, a Christian, has been reluctant to tackle the issue.
Local opponents of the code see it as violating the rights of women and preventing freedom of belief and freedom of association in some of the states where it is most strictly adhered to.
Aliero was at pains Friday to say non-Muslims would not be affected.
But such concerns would not prevent the state from fully implementing the code, he told the ceremony, attended by the Sultan of Sokoto and several other northern governors.
"As full implementation in this state commences, I reiterate government's ban on alcohol, prostitution, gambling and all forms of vices in conformity with the provisions of Sharia," the governor said.
The governor said that, in the Sharia code, the government was also announcing a ban on children trading on the street and had made it compulsory for children aged 5-12 to go to school.
"To protect children against delinquency, the state government has henceforth banned child hawking of any kind and to fight illiteracy made it compulsory for children aged 5-12 to attend school," he said.
Kebbi is the latest of nine northern states to declare Sharia since the country returned to civilian rule last year.
The trend began in October 1999 with the declaration of the Sharia in Zamfara State. Last Sunday, the north's most populous state, Kano, formally began operation of the system.
Since January this year, the code has been in actual operation in Zamfara and several other states. One man has had a hand amputated and several others been flogged for various offences.