Thousands of Real Madrid fans piled into the streets of the Spanish capital and filled the club's 80,000 capacity Santiago Bernabeu stadium on Sunday to welcome home their heroes after an historic 11th European Cup win.

An open top bus emblazoned with the word "Campeones" (Champions) carried the team, who showed off the trophy to fans, just after sunrise on their return from beating local rivals Atletico Madrid in a penalty shootout in Milan.

"How can I not love you!," shouted the ecstatic crowd at the Plaza de Cibeles -- a traditional meeting point for Real's trophy celebrations.

The Real players, who arrived home from Milan around 6:00 am (0400 GMT), headed directly for Cibeles where the fans had been celebrating since midnight.

The squad snapped photos of the raucous crowd from a platform specially erected at Cibeles before captain Sergio Ramos waved the large silver trophy for the cheering supporters.

Later after being greeted by Madrid mayor Manuel Carmena and heads of local government, the team returned to a full Bernabeu for a spectacular light and fireworks show.

Three-time World Player of the Year Cristiano Ronaldo struck the winning spot-kick after the two sides couldn't be separated with the score at 1-1 after 120 minutes of play.

It is the second time in three years that Real have defeated Atletico in the final.

"To win two Champions Leagues in three years shows that our efforts have had their reward," said Real captain Sergio Ramos.

"We are the best club in the world."

'Unforgettable and gruelling'

The football-mad Spanish capital of 3.2 million people had been dominated by the two clubs crests and colours in a frenzied build-up to the final, which attracted a worldwide audience of 180 million people in more than 200 countries.

Praise poured in for Real Madrid, including from Spain's acting Prime Minister Mariano Rajoy.

"Epic final in the League of Champions," he tweeted. "Congratulations to all... for the 11th."

However, there were mixed emotions for fans in the city as Atletico -- who have never won the Champions League -- lost in the final for a third time.

"I am delighted. Two Champions League titles in three years, it is incredible," said Monica Gonzalez, a 25-year-old Real fan.

"They (Atletico) deserved it. They almost played better. I am happy my team won, but it could have been any of the two teams."

However, Gonzalez's boyfriend Jaime de Francisco, an Atletico fan, couldn't hide his disappointment as once again the red and white half of Madrid was forced to life in Real's shadow.

Just 500 metres (yards) away from wild scenes of celebration at Cibeles, the Neptuno fountain -- where Atletico fans go to celebrate their triumphs -- was empty.

Spanish daily sports newspaper Marca captured the mood, describing Real as "the king of Europe", adding that manager Zinedine Zidane had been "touched by a magic wand".

"He was born to play for Real Madrid... and to lead them," wrote the paper.

"A supreme derby, exhausting, stifling," wrote the AS sports newspaper.

Spain's bestselling El Pais newspaper described the final as "unforgettable and gruelling", with an editorial arguing that Atletico have nothing to regret, saying that they were "far superior at the start, (and) must be gritting their teeth".

Real Madrid's Sergio Ramos kisses the UEFA Champions League trophy during celebrations of the team's win on Plaza Cibeles in Madrid with thousands of fans. Photo: AFP