The Italian musician topped the charts in 12 countries with the track, which was first released in 1995 and reached number two in the UK in 1996.
He also won the Brit Award for best international breakthrough act in 1997.
Pete Tong led the tributes to the DJ, who died in Ibiza, tweeting: "Sad to hear Robert Miles passing. RIP, thanks for the music."
Singer Boy George wrote: "R.I.P Robert Miles. Very sad news!"
The news was broken by producer and longtime friend Joe T Vannelli, who said: "The tragic news of the death of a very talented artist of our time makes me incredulous and upset.
"I will miss the fights, brawls, criticism, judgements but especially your talent in finding sounds and melodies unparalleled."
Miles received his Brit Award from Gary Barlow and Louise Redknapp
His statement continued: "I remember 1997 Brit Awards Ceremony very well. Robert Miles was the best international newcomer award, introduced by Gary Barlow. Miles was the only one Italian artist winner in BA history.
"Children is an instrumental and dance anthem, one of the most ever loved tracks. With Robert Miles a part of my life dies with him."
Miles was born Roberto Concina in Switzerland on 3 November 1969 to Italian parents.
'Thanks for the inspiration'
After finding mainstream success with Children, he had two further UK top 10 singles - Fable and One & One - and went on to release five albums.
He also launched a Balearic radio station called Open Lab, which played experimental music.
Other figures in the dance music community to pay tribute included Darude, who tweeted: "RIP Robert Miles. Thank you for the inspiration, direction & courage!"
Armin van Buuren said: "Really in shock to hear the news of the passing of Robert Miles," while Chicane wrote: "I only played 'Children' 2 weeks ago on Sun:sets.... I wished I had written it."