The Breakfast Show host had planned to marry the 30-year-old later this year, but they split after spending a fortnight apart.
Cox, who replaced Zoe Ball on Radio 1's flagship show at the end of March, said she still loved Thornhill and there were no hard feelings.
"It's been about as mutual and friendly as it could possibly be, but we're both gutted.
"We've had a brilliant three years together and nothing is going to change that," she added.
The couple became engaged on New Year's Eve 1998 and were virtually inseparable at celebrity bashes - often making up a foursome with Ball and her husband Norman Cook, aka Fatboy Slim.
Cox, 25, shot to fame as a presenter on Channel 4 The Girlie Show, before a stint on The Big Breakfast.
She beat off several rivals to land the top job at Radio 1 and her move has already been praised by critics.
Prodigy
Thornhill enjoyed enormous success with the Prodigy, who grew from playing a low-key gig in Dalston, East London to become the world's biggest dance act.
The 6ft 7in performer announced he was quitting the band last month to pursue his own projects.
It was when he came back from a stint filming abroad that the engagement was broken off.
Cox said: "Leeroy has been away in Belgium and Holland filming with BBC Choice for a couple of weeks and it was during that time apart that we came to this decision.
"Both of our lives have changed a great deal since we first met. We're just really relieved that we have finished it before we finished each other."