The Spain international played a major role in Saturday night's 4-1 Champions League final win over rivals Atletico Madrid by scoring a headed injury-time equaliser to send the match to extra time.
Madrid eventually went on to win 4-1, thanks to further goals from Gareth Bale, Marcelo and Cristiano Ronaldo, and Ramos has set his sights on bringing more trophies back to the Spanish capital - dismissing speculation of a potential transfer in the process.
"I feel privileged to participate in the world's best team," the former Sevilla defender told reporters. "I hope to be here for many years and retire here.
"From the first day here I noticed the affection of the fans and I will always be grateful. Winning the Champions League's a dream fulfilled."
The 28-year-old has a contract with Madrid until the summer of 2017.