Camavinga signed a six-year contract with Madrid in a deal reportedly worth up to €45million, having also been linked to the likes of Manchester United and Paris Saint-Germain.
After his big move, the 18-year-old France international reflected on the transfer to the Santiago Bernabeu.
"It's a dream I had when I was a kid. I can't wait to discover the stadium, which is very impressive," Camavinga said.
"I hope to play there as soon as the building work is finished."
Camavinga made 71 Ligue appearances for Rennes and 88 in total following his debut in 2019.
At 18 years and nine months old, he is the youngest outfield player to feature in that many games in France's top flight since Basile Boli in 1985.
In making his senior France debut on September 8 last year, Camavinga was the youngest player to do so since Maurice Gastiger against Luxembourg 107 years ago.
Only Gastiger (17 years and five months) scored for Les Bleus at a younger age than Camavinga, who was 17 years and 11 months old when he netted against Switzerland last October.
In 2019-20, Camavinga's breakthrough season at Rennes, he attempted 105 tackles in top-flight football. Among midfielders in Europe's top five leagues, only Declan Rice (116) and Wilfred Ndidi (129) attempted more.
"My move to Real Madrid was done very quickly. I am very happy and proud," Camavinga said.
"But I don't want this announcement to change my work with [France's] under-21s. Whether I play at Rennes or at Real Madrid I will continue to give my best, and of course I dream of the senior team, but step by step.
"Now I'll go to Rennes to pack my bags, I'll move to Madrid and I'll continue on my journey."