Madrid confirmed the acquisition of Tchouameni last week from AS Monaco in a deal worth an initial €80 million, with sources confirming to ESPN the European champions saw off competition from PSG and Liverpool to land the midfielder.
Mbappe himself turned down interest from Madrid earlier in the summer to renew his contract with PSG, but he could not persuade his France teammate to do the same.
"Kylian decided to stay at PSG and he knew I was leaving Monaco," Tchouameni said at his presentation as a Madrid player on Tuesday.
"He wanted to know if I would join him at PSG. But my first choice was Real Madrid and he understood that completely."
Tchouameni, 22, has signed a six-year contract at the Santiago Bernabeu and said that despite interest from PSG and Liverpool, he was sold on Madrid from the start.
"I had the chance to choose other teams but once I knew Real Madrid were interested, I did not have a single doubt," he added.
"I spoke with other clubs but in my head I was always waiting for Madrid. I spoke with my agent, my family and [Monaco] to find the best agreement for everyone.
"Madrid are the biggest club in the world, they have a team with incredible players and I think it's the best decision for me."
"There were already negotiations with Madrid at that stage," he said of watching those knockout ties.
"Then when I saw the games against PSG, Chelsea and City, I wrote to people saying: 'Please, do what you can so that I can go to Real Madrid!'"
Tchouameni, who will inherit Gareth Bale's No. 18 shirt, is seen by Madrid as a potential long-term replacement for Casemiro, 30, and will form part of a new midfield generation at the Bernabeu alongside Federico Valverde (23) and Eduardo Camavinga (19).
"He is one of the best midfielders in the world," Madrid president Florentino Perez said at the presentation.
"Today he arrives at Real Madrid. At 22 years old, he was able to choose his club and he chose this one."