Supporters, many wrapped in the club's flag, cheered as the squad arrived at Madrid's central Cibeles Square, the traditional home for raucous Real Madrid victory celebrations, in a white open-topped bus with the word "champions" written in black letters on its sides.

Fans applauded Real goalkeeper and captain Iker Casillas as, following tradition, he leant over the side of the bus and wrapped a Madrid insignia and club scarf around the statue of the Roman goddess that adorns a fountain in the square.

The victory bus drove three times around the fountain as fans twirled Real scarves in the air and took photos of the players.

"Winning the cup is fantastic, winning against Barcelona is even better," said Ezequiel Munoz, a 20-year-old student who came to the square with a group of friends after the match.

"We are going to celebrate all night long," added Munoz, who wore a black and white Real jersey with the name of the club's defender Sergio Ramos on its back.

Gareth Bale scored a stunning individual goal five minutes from time to secure Real Madrid's 19th Copa del Rey at the Mestalla in Valencia on Wednesday.

The jubilant crowd had started gathering around the stage set up by the fountain in the middle of the square as soon as the final whistle blew on Real Madrid's win.

The celebrating fans included large groups of teenagers, fathers with their young sons, elderly couples and a few people with dogs wearing Real scarves around their necks.

Fans chanted, set off firecrackers and danced in the streets while they waited for the players to arrive, as images of a football and a trophy along with the word "champions" were beamed onto the walls of city hall.

"I am very happy. I had no doubts that they were going to win because I saw that Madrid's defence was very tight and the counter attack was very well studied," said Juan Moreno, a 61-year-old Venezuelan plumber who waved a large Real Madrid flag.

After failing to win the cup competition between 1993 and 2011, Real Madrid have now won it twice in the last four years.

"Real Madrid is the best club in the world, they deserve this win, they are playing very well," said Adel Aboukar, 24, sporting a black blazer and jeans as he joined the celebrations with a friend after watching the match in a nearby bar.

Madrid city hall deployed 170 police to monitor the celebrations. 

Emergency services said they treated 16 people for dizziness, anxiety attacks and minor injuries, mainly cuts and bruises due to falls.

Real Madrid's win made the front pages of Spain's newspapers on Thursday.

"Bale's Cup," wrote centre-right daily El Mundo on its front page while top-selling daily newspaper El Pais wrote "A ray from Bale decides the Cup" below a photo of Casillas raising the trophy in the air.