The club chief believes that the Blancos have signed the star player of the World Cup and the midfielder hopes he can help the team win back-to-back European titles
The 24-year-old starred at the World Cup for triumphant Germany and was subsequently linked with a move away from Bayern Munich to the Santiago Bernabeu, where the Champions League trophy currently resides after May's Decima triumph.
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"[Recently departed Madrid legend] Alfredo Di Stefano would have been excited about Toni Kroos," he told reporters. "In Brazil, he was the most complete player of the tournament.
"His excellent performance in recent weeks were not a surprise for us, but just a confirmation that we chose the right man. He had a spectacular World Cup.
"Kroos is a young winner with an impressive record. He came from a friend of the club who are also a champion. Bayern imprint a special character on to those who wear their jersey. But this is your home now, Toni. This is your family.
"Now it is you who must give your best. Here the word 'impossible' does not exist. I want to thank you for choosing our club among the many alternatives you had.
"Two months ago we were celebrating our 10th Champions League, but Real Madrid always want more. Many, if not all, of us are already dreaming of the 11th Champions League now. I expect you to fulfil big dreams here. "
Luckily for Madrid, Kroos also shares a burning desire for further Champions League glory - he won the European trophy in 2012-13 - and believes he has made the right decision to part ways with Pep Guardiola and Co. at the Allianz Arena.
"First of all, I want to express my deep sorrow for the loss of Di Stefano," he said. "I know how much he meant for Real Madrid.
"I am incredibly proud to be here. I cannot imagine anything more beautiful that being here, with the Real Madrid fans. I want to thank the club for giving me the opportunity to come to play here, at the biggest club in the world.
"Thanks also to Bayern, who have given me the opportunity to take this step I wanted. It was the correct one. I'm proud. I know that Real Madrid have to win titles, but I already know what that pressure is like.
"In 2012-13 I won the Champions League with Bayern, in 2013-14 it was won by Real Madrid, and I hope that we can win again this year. I'll give everything for Real Madrid. Hala Madrid!"