Their charter aircraft was grounded at Stansted Airport in the south of England by technical problems.
The squad had to stay an extra 24 hours whilst the Nigerian government arranged a replacement flight.
The Nigeria Football Federation (NFF) issued an apology for the delay.
“We apologise to the federal government and the good people of Nigeria for this charter company’s failure,” Bolaji Ojo-Oba of the NFF said.
“(We also apologise to) the Nigerian High Commissioner to South Africa and the staff who went through considerable discomfort waiting for the team to arrive on Tuesday.
“We didn’t want the team to fly on a regular airline with its complications and unpredictability.
“The players fly business class; it would have been difficult for us to secure in excess of 40 business class seats on one aircraft.
“Whatever we did was in the interest of the team, their safety, security and comfort.
“What has happened is unfortunate, but we are full of gratitude to the federal government for its keen interest in this matter.”
Nigeria will take on North Korea on Sunday in their last warm-up before opening their World Cup campaign against Argentina on 12 June.
They also face South Korea and Greece in Group B of the World Cup.— BBCOnline.