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.
Miles's radio station OpenLab confirmed he died "after a courageous battle with stage four metastatic cancer".
Pete Tong led the tributes to the DJ, 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 won the Brit Award for best international breakthrough act in 1997.
Vannelli's 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."