The former Take Me Out host had fronted the long-running BBC show with Chris Harris and Freddie Flintoff since 2019.
The Grand Tour presenter admitted he'd been "saddened" by the news.
The BBC said it knew its decision "will be disappointing news for fans", but insisted it is "the right thing to do".
Top Gear ceased production on its upcoming series following the accident in December 2022.
The BBC has issued a public apology to the presenter following the accident in December last year.
"We are all shocked but just hope he’s going to be OK.”
The incident happened on Tuesday morning at Dunsfold Aerodrome in Surrey.
The Top Gear star suffered an unfortunate consequence during a 2012 bike ride.
He won the show, but he didn't exactly stick to the rules.