Gold-winning medal cyclist Chris Hoy was joined by fellow Scots medallists Ross Edgar, Katherine Grainger and David Florence for an open top bus parade down Edinburgh's Royal Mile.

The historic thoroughfare was packed with flag-waving well-wishers as the bus made its way from Edinburgh Castle, where a reception for the Olympians was held, down to Holyrood Park.

"It means so much to be home but also to see how warm the reception has been and how much interest there has been," Hoy said today.

"We had no idea in the village just what was going on.

"You get the odd text message and email saying it's crazy, but you just don't take it in."

Hoy, 32, became the first Briton for 100 years to win three golds at a single Olympics, having previously hit gold in Athens four years ago.

The athletes waved to the crowds from the top deck of the Saltire-clad bus, with Edinburgh native Hoy picking out friends and relatives below.

Edinburgh's Lord Provost George Grubb said the parade through the heart of the capital had been a "staggering success".

He added: "Everyone who came out today had a fantastic time.

"Many more people came along than we had expected and it was perfect opportunity to welcome the medallists back – I think people will be talking about it for quite a long time.

"The huge turnout at the Royal Mile is a sign of how proud Edinburgh people are of our athletes and of the massive impact that Chris Hoy has made on the global stage."

The council later estimated 50,000 had turned out.

Among the crowd was Jennifer Davidson, 28, from Bearsden, near Glasgow, who had come to Edinburgh on her day off work to cheer on the athletes.

"They really deserve all this," she said.

"In fact, I think they deserve a lot more.

"We just can't do enough to show them how much we appreciate their success."

Mark Holloway, 44, was visiting Edinburgh on holiday from Suffolk.

He said: "This is a great event. You can't do enough for them. It's just fantastic. I feel very emotional about it. I'm so proud.

Scotland's Deputy First Minister Nicola Sturgeon was among the dignitaries to welcome the athletes home at Edinburgh Castle.

"We are really immensely proud of all of you," Ms Sturgeon told the four Olympians.

"We're quite overawed by the sheer scale of your achievements."

Ms Sturgeon referred to a huge multi-storey poster of Hoy which has been erected in Edinburgh city centre with him holding a bike above his head in front of Edinburgh Castle and the words "King of Scotland" emblazoned along the bottom.

"I don't think there's anybody in Scotland who would disagree with that title right now – you are absolutely amazing."

Edgar, 25, who clinched silver in the men's Keirin behind Hoy, described winning the medal as "the biggest thing that's ever happened in my life".

He went on: "Just to be in the same era as Chris, it's an amazing thing."

Rower Grainger, 32, picked up her third silver medal in three consecutive Olympics.

Asked whether she would be competing in the London 2012 Games, she said: "It's only two days since Beijing so it's quite early to make any decisions.

"Anyone who's been to an Olympics would agree it's the most inspirational, exciting thing to be part of."

Canoeist Florence, 26, spoke of the moment he took a silver medal in the men's slalom.

"The run went fairly well fortunately in the final. We came to the bottom and crossed the line and that was it," he said.

"That was 10 years of pressure over."