After receptions with King Felipe VI and prime minister Pedro Sanchez, La Roja were paraded through the capital city on an open-top bus.
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.
"It's hard to put into words how we're all feeling right now... We did well to get back into the game and struggled to build on that," added Kane.
Yamal, 17, and Williams, 22 -- both celebrating birthdays in the days ahead of the final -- have given Spain an exciting cutting edge in attack they have lacked for much of the last decade, pulling the team to a record fourth European Championship triumph.
"Right now, we don't realise what we've done. We'll return to Spain tomorrow and will be able to live this thing with the fans and return love and the warmth they've given us."
Spain won all seven games in Germany en route to lifting the trophy, but England gave them a hard fight in the final, losing 2-1 to a Mikel Oyarzabal goal four minutes from time.
Southgate gave his penultimate press conference of the tournament in the bowels of Berlin's Olympiastadion just over 24 hours before his team will run out seeking to finally win another major trophy to go alongside the 1966 World Cup.
"I've told my mum that if we win I don't want any presents, I just want to celebrate in Madrid with my mates," Lamine, as he prefers to be called, said in an interview with Spain's Marca outlet on Saturday.
It's not yet midday but there is a real buzz inside the local bar, El Cordobes, which is still reeling with excitement after Yamal, who used to come in with his dad, clutching a football, shot home the sublime goal against France that helped propel Spain to Sunday's Euro 2024 final.
The Three Lions were already assured of a place in the last 16 but can expect more criticism after failing to improve on underwhelming performances in edging past Serbia and drawing with Denmark.
The 38-year-old became the oldest goalscorer in European Championship history when he prodded home in the 55th minute to put Croatia on track to reach the knockout phase for a fifth straight major tournament.
Spain matched their feat of 2008 when they also won every group game on the way to the title
Deschamps kept his cards close to his chest on the French Telefoot television programme, declining to say if Mbappe would feature against Poland in Dortmund but offering reassuring news for supporters about the recovery of his captain, who fractured his nose last Monday in their opener against Austria.
"We have a new team with a lot of young boys. I'm already getting a little older and I want to show with the Devils in my last years how to behave as a player and as a leader," he said.
Saba Lobjanidze could have won it for Georgia at the death but blazed his shot over the bar after a breakaway and both sides, with one point from two games, need a win in their final Group F match to progress to the knockout stages.
Ronaldo is Portugal's all-time top scorer with 130 goals in a record 208 international appearances and is playing at his sixth European Championship at the age of 39.
Shaqiri produced one of the goals of the tournament so far as the former Liverpool forward punished Anthony Ralston's woeful backpass with a brilliant curler from 20 yards.
Both sides came into the game in desperate need of points having lost their openers, but in the end they shared the spoils - to the Albanians' delight and the Croatians' despair.
Hungary, considered by many the second-best side in the group, were soundly beaten 3-1 by Switzerland in their first game and will slide close to elimination should they lose again on Wednesday.