The 27-year-old moved to Los Blancos for around £51.8 million, four years after moving to Stamford Bridge from Brighton.
Cucurella always expressed his desire to return to Spain, and when Real Madrid came calling - quite literally - he couldn't turn down the opportunity.
"When Madrid came I didn't think about it, it's a unique opportunity. Playing for Real Madrid is an honour and not many players can say it, so I had no doubts," he told Spanish outlet El Mundo.
The talented defender also revealed what Jose Mourinho told him in a phone call before agreeing a switch to the Spanish capital.
"He told me that he really wanted to work with me, that I was going to adapt very well, that Madrid was a great club. I am looking forward to working with him," Cucurella added.
Mourinho recently returned to Real Madrid, 13 years after being sacked by president Florentino Perez, who won the election against his rival, Enrique Riquelme.
Cucurella joins three high-profile players at Real this summer. Bernardo Silva and Ibrahima Konate have already been confirmed, while Denzel Dumfries is set to follow.