Pictures show his coffin being delivered to the St Stephen’s cathedral – with his famous red helmet laid in a wreath atop the wooden casket.
Austrian-born Lauda was the only driver to have been a champion for both Ferrari and McLaren.
He was a three-time Formula One World Drivers’ Champion, winning in 1975, 1977, and 1984.
The 70-year-old passed away before the Monaco Grand Prix, where his close pal Hamilton went on to win.
Lauda was key part of the Mercedes team which have dominated the sport since 2014.
He is reportedly set to be buried in his famous Ferrari race suit, driving for the team from 1974 to 1977.
Lauda was receiving kidney dialysis at a private clinic in Switzerland.
Tributes poured in for the F1 great lead by Hamilton, who hailed him as a “bright light” in his life.
And after winning in Monaco, the five-time world champ said: “I was fighting with the spirit of Niki.
“He has been an influential person in the team. I know he was looking down.”
Lauda was famously badly burned in a horror crash during an F1 race at the Nurburgring in 1976 – a circuit he had already warned was too dangerous.
Fellow drivers Arturo Merzario and Guy Edwards pulled him from the flaming wreckage of his Ferrari after a shocking crash.
But he returned to racing just six weeks later, narrowly missing out on the world title to James Hunt.
He would go on to win the championship twice more, the following year in 1977 and during his comeback second career in 1984.