It had earlier been reported that the presenter, who will join ITV later this year, might not return to show following a break if a replacement was found in time.
A statement said: "Following the BBC's decision to withdraw its offer of an extended contract to Christine Bleakley, we have agreed she will not be returning to The One Show.
"The BBC would like to take this opportunity to thank Christine for her contribution to the show and to wish her well."
The 31-year-old presented her final show on June 10 with Matthew Allright.
The corporation confirmed that guest hosts will take over the show on its return on Monday, July 12. Jason Manford, who takes over from Adrian Chiles, will begin presenting with Bleakley's replacement next month.