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.
In a statement, European football's governing body UEFA said that Bellingham would be fined 30,000 euros ($32,477) and suspended "for a total of one UEFA competition match for which he would be otherwise eligible for violating the basic rules of decent conduct".
Demiral scored two goals in the 2-1 last 16 win over Austria on Tuesday and during celebrations for his second goal made a gesture associated with Turkish right-wing extremist group Grey Wolves.
"It is an honour. Everyone knows about my admiration for Cristiano," France captain Mbappe, 25, told reporters on the eve of the Euro quarterfinal game against Portugal.
Copa favourites such as reigning champions Argentina and Brazil advanced to the quarter-finals playing in sold out stadiums but the less heralded teams have played in half-empty arenas.
Forward Joselu heaped praise on last season's teammate at Real Madrid, but said Spain were laser-focused on winning in Stuttgart to reach the Euros semi-finals regardless of the implications for Kroos.
Earlier, European soccer's governing body UEFA opened an investigation into the Turkish centre back's celebration in a Tuesday evening match that Germany condemned as racist due to its far right associations.
Kroos, who won the Champions League with Real Madrid last month and will hang up his boots after the Euros, came out of international retirement this year to chase the one major trophy missing from a vast haul that also includes the 2014 World Cup.
The Al-Ahli centre-back smashed home after just 58 seconds and produced a towering header on the hour mark to double Turkey's lead.
After a goalless draw over 120 minutes of the last 16 clash in Frankfurt, Porto goalkeeper Costa produced three saves to thwart Slovenia's three takers as his team claimed a 3-0 shoot-out win.
Ronaldo broke down in tears after missing a penalty in the first period of extra-time in the goalless tie in Frankfurt.