The midfielder, 27, was detained on Sunday after police received reports a cyclist had been struck by a car which then hit a pump at a petrol station.
Mr Gibson is accused of driving with excess alcohol, after the crashes in Altrincham, Greater Manchester.
He is due before Trafford Magistrates' Court on 1 September.
A Greater Manchester Police spokesman said the cyclist was unhurt.
It is alleged he was behind the wheel of his black Nissan Skyline GT-R Nismo car when the crashes happened close to his home.
Greater Manchester Police said Mr Gibson was charged with driving without due care and attention, driving with excess alcohol and failing to stop after a road traffic collision.
"This is in relation to an incident on Sunday August 16 where police were called to reports that a car had collided with a cyclist on Park Road, Trafford, and failed to stop before pulling into a petrol station on nearby Dunham Road and colliding with a pump," a spokesman said.
Londonderry-born Gibson began his career at Manchester United before joining Everton in 2012 for a fee of about Â£1m.  He is currently recovering from a groin injury.
An Everton FC spokesman declined to comment.
Everton and Republic of Ireland star Darron Gibson has been charged in connection with an alleged hit-and-run crash with a cyclist.