The 27-year-old winger signed a two-year deal with the Magpies in July 2015, arriving from Dutch side FC Oss, but has agreed to end his contract early.
The Dutchman made 25 appearances for Notts, scoring four times including a stunning volley at Morecambe last season.
Snijders said: "I would like to thank the Notts County fans for their support during my time here. They have been amazing with me from the first day I signed.
"I wish this fantastic club well in the future and hope our paths cross again soon."
Notts County thank Genaro for his contribution in the black and white stripes and wish him all the best for the future.