Giant-Shimano's Kittel will wear the race leader's yellow jersey on Sunday's second stage after triumphing in the run from Leeds to Harrogate.
Prince William, his wife Catherine and Prince Harry took part in a royal opening ceremony in Leeds before the 2014 Tour began.
The Duchess of Cambridge was given the honour of cutting the official start ribbon at Harewood House just outside Leeds before reigning champion Chris Froome and the rest of the peloton set off on the 190.5km opening stage around Yorkshire.
Tour de France riders and organisers meanwhile praised the "amazing" crowds in Yorkshire but pleaded with people to take more care of their safety.
The number of people standing by the side of the roads along the 190km course stunned many observers but several riders said their enthusiasm had got the better of them.
Marcel Kittel said that while it was great to see, they needed to be more wary of their safety.
"There were some moments when I thought, now we will crash because the spectators were taking pictures and didn't see that they were in the centre of the road," he said.
"It's very important to tell people we are of course happy to have them there, they were an amazing crowd, it was really amazing to see them there, but they really have to take care of themselves and stay off the road and look after their children."
Tour organisers took to Twitter to plead with people to be more careful, saying: "SECURITY MESSAGE: please stay beside the road during the race." German sprinter Andre Greipel also griped about the overzealous fans lining the streets.
He tweeted: "I appreciate people coming to support us + making an incredible feeling 4 us along the road but please stay beside the road not on the road."
Not everyone thought it was a problem, though.
Australian Simon Gerrans crashed in the sprint finish when he came together with Briton Mark Cavendish but he had nothing but praise for the supporters.
"The crowds were unbelievable, it's not too many times in my career that I've raced in front of crowds as big as we've had today," he said.
"It's a bit of a buzz racing in front of so many people."
Some people compared the crowds on the Yorkshire Dales with the throngs usually seen in the Alps or Pyrenees.
Garmin Sharp's American manager and former racer Jonathan Vaughters tweeted a picture of the crowds with a message: "Crowds were truly incredible today. Biggest I've seen outside l'alpe d'huez."