Both opponents have qualified for Russian Federation 2018 and Southgate believes the games will set-up his stars for a successful tournament.
"But it's not just about the games we've got in the group stages, but hopefully beyond that as well".
The Three Lions will play the Super Eagles five days before facing Costa Rica in another friendly at Elland Road.
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England have finalised their World Cup warm-up programme and will face Costa Rica at Elland Road in their last game before heading to the tournament.
England topped their group in qualifying and coach Southgate sees the Nigerians and Costa Ricans as ideal preparation for two of their first round opponents Tunisia and debutants Panama.
England defeated Nigeria 1-0 in a highly entertaining friendly at the old Wembley in 1994 with David Platt scoring the only goal. "All of the feedback from the team before Euro 2016 was really positive, the players enjoyed it and it was definitely well received by the public", added Southgate.
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The match will take place on Thursday 7 June at 8pm and it will be the third time that the national team have played at Elland Road.
"We have a huge following in Yorkshire with large numbers of our members and traveling support coming from that area".
England will play two warm-up games in June before flying to Russian Federation, with the Football Association also set to confirm a Wembley friendly against Nigeria on June 2.
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