James Bays, Al Jazeera's correspondent in Madrid, said: "The streets are thronged with people. There are literally thousands of people.
"The temperatures are above 40 degrees, we've had the fire brigade here dousing them with water to keep them cool.
"Everyone is overwhelmed by the atmosphere, so excited to be here ... this the most important victory in Spanish sporting history."
"Thank you champions, in the name of all of Spain and all Spaniards," said the king after personally greeting each of the players.
"This is a well deserved victory for an exceptional team which thrilled the hearts of all Spaniards.
"You brought together all Spaniards, made our dreams a reality and projected the name of Spain the world."
The king, accompanied by his wife Queen Sofia, was presented with a red team jersey signed by all the players by Casillas.
Andres Iniesta's goal with four minutes to play in extra time against the Netherlands on Sunday allowed Spain to lift the World Cup for the first time in its history, while becoming only the eighth team to win world football's most prized title.
'Kings of the world'
After an all night party, Madrid went back to work on Monday feeling groggy but basking in the satisfaction that "La Roja" (The Reds) were champions of the world.
National newspapers headlines hailed the winners with daily La Vanguardia carrying a simple headline, "Kings of the World", over a photograph of Iniesta holding the World Cup.
On their way to work, Madrid residents expressed their satisfaction.
"Well, pride, happiness and satisfaction, especially at a time when people are questioning the unity of this country," said one man, referring to Catalonia, where people are demanding more autonomy for the region.
According to consultants Barlovento, 14 million people watched the 1-0 win on television, with the extra-time period the most viewed Spanish broadcast ever, peaking at 15.6 million, or roughly 38 per cent of the country.
Officials said about 75,000 fans celebrated in Barcelona on Sunday night, where more than 1.1 million people had protested a day earlier against a Spanish court ruling that the Catalan region was incompatible with a united Spain.
The Barcelona celebration turned ugly after midnight when fans threw bottles at riot police, prompting officers to disperse them with volleys of rubber bullets.
No serious injuries were reported.