But Kano state is at the same time banning alcohol and prostitution, reports from the state say.
The 19 governors from the predominantly Muslim north also decided to set up a Muslim-Christian committee to look at implementing aspects of Islamic law not covered in the penal code.
In February, more than 1,000 people died in bloody clashes between Christians and Muslims following protests against implementing Sharia in Kaduna state.
The violence prompted the federal government to announce that the Sharia penal code would no longer be implemented.
But several northern states vowed to press ahead with plans to introduce the strict Islamic law, already in force in Zamfara state since January.
The authorities in Zamfara recently carried out their first amputation on a man found guilty of stealing an ox.
Previously, Sharia courts had flogged a man found guilty of drinking and another man found guilty of pre-marital sex.
Unity move
In a joint statement, the 19 governors said they intended to make northern Nigeria "one indivisible geo-political entity" within the country's federation of states.
The issue of Sharia was felt to be alienating more moderate Muslim states from those which wanted to introduce Islamic law.
The northern states decided to revert to the penal code in force since colonial days.
They also said the committee would look at unspecified differences between the 1979 and 1999 constitutions concerning Islamic law, which stipulate the country is a secular state.
Alcohol ban
But officials in Kano announced they were banning prositution, gambling and the sale of alcohol, in an attempt to reduce social problems and the incidence of Aids.
Kano state includes the main northern city of the same name, and has a large minority Christian population.
A leading human rights lawyer has launched a case to test the legality of implementing Sharia, arguing that it violates the secular nature of the constitution.
But President Olusegun Obasanjo, a devout Christian, ruled out similar legal moves by the government, saying that to do so would be divisive.