The talented midfielder made the move for an undisclosed fee on his 19th birthday, writes Tom Feaheny.
Crawford impressed within the academy and after a couple of loans spells as well, he stepped up to the first-team and hasn't looked back.
In total he made 17 appearances for the side and scored on the final day of the Vanarama National League season as Chester defeated Barrow 2-1.
Just this past weekend he made his debut for England C where he came off the substitutes bench in a 4-2 loss to Ireland Amatuers in Dublin.
“I loved every minute of my time at Chester and I was disappointed we went down,” Crawford told Notts County's website.
“But, for me personally, to get into the team and play 17 games and score a goal was a big achievement.
“I’ll be working my socks off between now and pre-season to be fitter than ever before.”