Chiles's new ITV job, understood to be worth 1million a year, will see him front GMTV and ITV's football coverage in a four-year deal.
The 43-year-old, who appears on The One Show and other BBC programmes, will lead ITV's World Cup coverage in June, including England's two peak-time opening games.
From next season, the exclusive ITV deal will see him front the Champions League, England's home internationals and away friendlies and the FA Cup.
Rider, who turns 60 this month, joined BBC Sport in 1985 and was at the corporation for 20 years, presenting more than 700 editions of Grandstand, as well as covering summer and winter Olympic Games, before joining ITV in 2005. His deal is said to be due to end this year. Asked about Rider, ITV said: "We're talking to Steve about future options."
Chiles left the BBC after Chris Evans was drafted in to host The One Showon Fridays. Chiles's BBC contract has a month to run. He said: "It's no secret how disappointed I was by the decision to change a well-loved show."