It is the first West African contingent to join France’s anti-rebel operation launched in Mali on Friday.
In total, 3,300 regional troops will be deployed in the conflict under a UN Security Council resolution. Chad has confirmed it will send 2,000 troops.
Meanwhile French and Malian forces have started the first major ground operation against the militants.
Sources say street battles broke out between soldiers and rebels in the town of Diabaly, 350km (220 miles) north of the capital Bamako on Wednesday.
Islamists entered Diabaly on Monday, taking the town from Malian forces. French fighter jets have since attacked the rebel position.
A company of 190 Nigerian soldiers will be flown from the northern city of Kaduna into Mali on Thursday, the BBC’s Will Ross in Kaduna reports.
Nigeria will lead the West African regional force. It has promised to send a total of 900 troops as well as fighter jets.
Chad has also confirmed 2,000 soldiers will join the anti-rebel operation in Mali.
“We intend to send an infantry regiment and two support battalions,” Chadian Foreign Minister Moussa Faki Mahamat told Radio France Internationale.
Benin, Ghana, Niger, Senegal, Burkina Faso and Togo have also pledged to take part.
France intervened in Mali last Friday to try to halt the Islamists’ push southwards towards the capital.
It has some 800 troops on the ground in Mali and defence sources said their numbers were expected to increase to 2,500.
However, France has been pushing hard for the deployment of a West African regional force.
The arrival of the first Nigerian troops should bring some relief to French soldiers who are only getting limited support from the fairly week Malian army, our correspondent says.
It is not yet known exactly what role the West African troops will play or how well prepared they are for what is likely to be a very challenging ground assault against the Islamist militants, he adds.
The UK has provided transport planes, and on Wednesday Germany gave two transport planes as logistical support.
‘We will not fire’
Meanwhile a convoy of 50 French armoured vehicles left Bamako on Wednesday.
“Until now, we had made sure there were a few ground forces in Bamako to keep our people safe. Now French ground forces are heading up north,” French Defence Minister Jean-Yves Le Drian said.
He admitted that Malian forces around Diabaly have been struggling to combat the well-armed rebels.
He added the central town of Konna had not been recaptured by government forces as had earlier been reported.
A Malian security source told AFP news agency that French special forces and Malian soldiers were fighting “hand-to-hand” with Islamists in Diabaly.
Adm Guillaud said France would do all it could to ensure civilians were not targeted. “When in doubt, we will not fire,” he said.
French President Francois Hollande said France had been right to intervene.
“If the choice had not been made, it would no longer have been a question of ‘when’, because it would have been too late,” he told journalists.
“Mali would have been conquered completely and the terrorists would be in a strong position today.”
Mr Hollande later said that France’s parliament would hold a vote on the operation if it had to be extended beyond four months.
In a separate development, the chief prosecutor for the International Criminal Court has opened a war crimes investigation, focusing on acts committed since January 2012 in some northern regions of the country.
“At each stage during the conflict, different armed groups have caused havoc and human suffering through a range of alleged acts of extreme violence,” Fatou Bensouda said.
“I have determined that some of these deeds of brutality and destruction may constitute war crimes.”