Gordon Strachan's side will bid to extend their unbeaten run to six matches when facing the Super Eagles, who came from behind to beat Scotland 2-1 at Pittodrie in the last meeting between the two teams in 2002.
The match is likely to be Nigeria's final warm-up game before they head to Brazil for their fifth appearance in the World Cup finals.
Scotland's recent revival continued with a 1-0 win over Poland in Warsaw on Wednesday, their fourth consecutive clean sheet.
Strachan is delighted to be facing quality opposition ahead of their daunting Euro 2016 qualifying campaign, in which they will face Germany, Republic of Ireland, Poland, Georgia and Gibraltar in Group D.
"We considered a lot of options but the chance to play Nigeria, a country who will be going to the World Cup this summer, in London without the need for long-haul travel was the one that appealed most," said Strachan.
"We will have time for some quality training sessions before the game and we will look to finish the season with a positive performance and result that we can take forward as we finalise preparations for the Euro 2016 qualifiers.
"I was encouraged yet again by a lot of what I saw in Warsaw and the players are now protective of the performances and results they have put together recently. We will look to continue that against Nigeria."