"This is the happiest day in the 25 years of my professional life and is a very important moment for me," Queiroz told a news conference at the Bernabeu, hours after signing a two-year contract to coach the nine-times European champions.
"(Former coach Vincent) Del Bosque's record will only act as an inspiration to me. I aim to use his example to help me improve the team and to meet the objectives set by the club."
Real surprisingly decided not to renew Del Bosque's contract on Monday just a day after he led the side to their 29th Spanish league title, but the former Manchester United assistant manager said he would not be overawed by his new job.
"It's not the time to make promises," he said. "But I aim to respond to the confidence that Real Madrid have placed in me. My motto is never to make promises, but instead deliver the goods."
Club president Florentino Perez said that the 50-year-old former Portugal and South Africa boss was the perfect choice to succeed Del Bosque.
"He is a coach with a philosophy and a set of qualities that respond precisely to the needs of Real Madrid," said Perez.
"He knows what Real Madrid is all about and understands that its fans are accustomed, not just to winning, but also to providing a great spectacle."
FERGUSON TRIBUTE
Queiroz, who had two years left on his contract with Manchester United, paid tribute to manager Alex Ferguson and the English club for allowing him to take the Real Madrid job.
"Alex Ferguson is a very special person," he said. "I knew that from working with him, but when I spoke to him about this opportunity he showed me real understanding and I will always be very grateful to him for that.
"I was honoured to work with both him and a great club like Manchester United."
Queiroz said he did not think the signing of David Beckham would cause a problem for Real's over-stocked midfield ranks.
"David is a great player and a great professional," he said. "He showed that when he was at United."
"I always think the best football is played by the best players and I will be trying to make sure they work in harmony. The only time I want to leave Beckham or Luis Figo on the bench is when they are injured."
He concluded by saying that his ultimate objective was to please the notoriously demanding supporters of the club.
"My aim at Real Madrid is to make the fans happy and if I do that then it will mean that I will be doing a good job."