The former Portugal and South Africa coach will be presented to the media at 1830 local time at the club's Bernabeu stadium.
Real made the surprise decision on Monday not to renew the coach Vicente del Bosque's contract, just a day after the club secured their 29th Spanish league title.
The appointment of Queiroz, formerly assistant to Manchester United manager Alex Ferguson, should make it easier for Real's new signing David Beckham to adapt to life at the Bernabeu.
Beckham, who is on a promotional tour in Asia, was bought from Manchester United for 35 million euros ($40.27 million) last week. He is due to be presented by Real on July 2.
A second raid on United is a major blow for Ferguson, who has been delighted with the contribution of Mozambique-born Queiroz since he joined the club 12 months ago.
But the United manager told the Daily Mail on Wednesday that he would understand if his assistant decided to move to the Spanish champions.
"This is a wonderful opportunity for him (Queiroz), too big a chance to turn down," he said.
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