The governing body has announced the Dark Blues will face the Super Eagles in London at the home of Barclays Premier League side Fulham.
Strachan's men are already on a high following Wednesday night's 1-0 win against Poland in Warsaw.
The Scots will continue their preparations for the Euro 2016 qualifiers against the Brazil-bound Nigerians, who have qualified for their fifth World Cup finals tournament.
The Polish victory was the fourth game on the trot that Scotland have kept a clean sheet and follows away wins over Croatia, Macedonia and Norway.
Scotland last met Nigeria at Pittodrie in 2002, when the Africans came from behind to win 2-1.
Scotland have been drawn against Germany, Republic of Ireland, Poland, Georgia and Gibraltar in Euro 2016 Group D.
Strachan believes the match against Nigeria presents another opportunity to test themselves against quality opposition before the group opener against Germany in September.
He said: "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.
"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."