Spain, the 2010 World Cup winners, were drawn against the Netherlands and 2018 world champions France were paired with Croatia in the two-leg quarter-finals in March.
Italy have been drawn to face Germany, while Portugal will play Denmark.
The eight teams advanced to the quarters by placing first or second in the four Nations League top-tier groups that finished this week.
Games will be played on March 20 and 23, and the winners advance to a Final Four mini-tournament scheduled for June 4-8. It will be hosted by one of the teams involved.
European champions Spain are also defending the Nations League title after winning the third edition of the biennial tournament last year.
"It's a fantastic match," Netherlands coach Ronald Koeman said. "Both teams like to play football, and we have a big history."
"We have a great respect for them and they have a great respect for Dutch football," added Koeman, whose goal won Barcelona their first European Cup in 1992 for a team coached by Dutch soccer icon Johan Cruyff.
France and Croatia are still coached as they were in 2018 by Didier Deschamps and Zlatko Dalic, who are now in their 13th and eighth seasons, respectively, as two of the most experienced coaches in world soccer.
France won that World Cup final 4-2 in Moscow and have met Croatia four times since in different editions of the Nations League.
"Obviously I've got a lot of affinity with Zlatko," said Deschamps, who has won three of his five games against Croatia. "We've often had the chance to talk and he's someone I appreciate very much."
Dalic said of Deschamps that he was "happy to see him again. I have full respect for France."
Croatia won 1-0 at Stade de France in June 2022 with a penalty from Luka Modric, who is still captaining the team, aged 39.
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