During the celebrations, which saw the city turned into a sea of red and yellow, several players grabbed the microphone to sing, with captain Alvaro Morata belting out "Gibraltar es espanol" -- "Gibraltar is Spanish" -- in a chant also picked up by Rodri, who plays for English club Manchester City.
Spain midfielder Rodri and 17-year-old Lamine Yamal were among six Spain players named in UEFA's team of the tournament for Euro 2024 on Tuesday.
Gareth Southgate leaves his job as the second most successful England manager in history but with a string of agonising near-misses to his name.
"My family has fought for this moment. This is for all of them, everyone who believed in me from the very beginning," said Williams.
After receptions with King Felipe VI and prime minister Pedro Sanchez, La Roja were paraded through the capital city on an open-top bus.
Switzerland's Xherdan Shaqiri announced his retirement from international football on Monday after winning 125 caps with the Swiss national team.
Spain coach Luis de la Fuente thanked his players for delivering a record fourth European Championship on Sunday, saying they always believed in him, while others didn't.
Substitute Mikel Oyarzabal became the 10th Spain player to score at Euro 2024 when he set up and finished in the 86th minute to secure a 2-1 win over England and a record fourth title. It was their 15th goal, the most by any team at a Euros.
England's quest for a first major tournament win in 58 years remained alive after another late fightback before beating Switzerland 5-3 on penalties to book their place in the Euro 2024 semi-finals on Saturday.
The Barcelona playmaker had to be substituted after just eight minutes in the clash in Stuttgart, which Spain won 2-1 after extra-time.
"It's sad that I'll probably never be a part of a home Euros in my career again," the coach said. "That hurts. And having to wait two years to become world champions, that hurts as well."
"I know the boss at times will come under criticism and come under stick, but, ultimately, it’s us on the pitch, to make the difference in vital moments," Kane told reporters.
“There is a high probability that this was my last international match,” said the 34-year-old.
Cody Gakpo and Arda Guler endured frustrating seasons but both have established themselves as their teams' vital players as the Netherlands face Turkey in a Euro 2024 quarterfinal clash on Saturday in Berlin.
England's European Championship campaign looked dead and buried before it was salvaged by a remarkable last-gasp goal from Jude Bellingham in the round of 16, but they have barely made their presence felt in Germany.
France coach Didier Deschamps savoured seeing his side win a penalty shoot-out for the first time since the 1998 World Cup as they beat Portugal in Friday's Euro 2024 quarterfinal after another difficult night for star man Kylian Mbappe.
Portugal manager Roberto Martinez said there was no blame to cast after Joao Felix missed the penalty that resulted in their exit from the European Championship and likely brought the curtain down on Cristiano Ronaldo's international career.
Germany coach Julian Nagelsmann lamented the decision to deny his side a late penalty in Friday's 2-1 Euro 2024 loss to Spain, saying "the referee blew in favour of Spain a little".