Sports Minister Leon Bignell joined several hundred Adelaide United fans who flocked to the city's CBD today to welcome players to an official reception.
It followed a massive celebration in Rundle Mall on Monday, where thousands of chanting fans applauded the players' efforts.
"Anytime at Adelaide Oval," Mr Bignell said to the crowd, taunting Leicester City to a match against the local Reds.
"I guess we could call it the Fairytale Cup.
"In the EPL, we had Leicester come from nowhere at the beginning of the season and we had Adelaide United win the Australian championship and the A-League title after losing their first eight games, so both fairytale championships.
"We think it'd be a great idea for them to get together to fight it out in the Fairytale Cup at the Adelaide Oval."
The Reds won the A-League grand final 3-1 against the Western Sydney Wanderers at Adelaide Oval on Sunday.
Adelaide's Lord Mayor Martin Haese said the win was impressive.
"This is the Reds' first grand final victory from 13 seasons in the A-League, so it's definitely cause for celebration," he said.
Adelaide United's chairman Greg Griffin said the season had been ground-breaking for the team.
"Winning the championship and premiership after our start to the season is a massive accomplishment, perhaps the most significant that we will see in Australian football for a long time," Mr Griffin said.
For the parade, the eastern side of King William Street between Flinders and Pirie streets will be closed to traffic until 2:00pm.
Sonia DiPardo, 44, was among the fans to take an early front-row spot in front of the Town Hall.
She said at Sunday's grand final, she and her father had a seat about five rows from the front at Adelaide Oval.
"It's just good to celebrate something good for South Australia," she said.
Ms DiPardo said she shed "tears of joy" at the game and while the Wanderers had about 10,000 fans there, they could not be heard.
Ryan Arlt, 25, said the win did not always look to be a sure thing.
"It was definitely not on the cards. We were eight-nil at the start of the season," he said.
"It was a fairytale season, definitely."