The Magpies will also play La Liga outfit Rayo Vallecano and former European Cup winners Steaua Bucharest, in a game behind closed doors, as they prepare for the League One campaign.
Magpies chairman Ray Trew told the club's official website: "A tremendous amount of hard work has gone on to secure top class opposition for our pre-season schedule and I couldn't be happier with the schedule that has been arranged.
"You only have to look at the players in Galatasaray's squad to see how big a draw that game is for any football supporter and followed less than a week later by the visit of one of Spain's top teams in Rayo Vallecano is a real coup for this club.
"Whilst the game against Steaua Bucharest will be held behind closed doors, being able to secure a game against such prestigious opposition as part of their pre-season plans is testament to the high regard that Notts County Football Club is held in throughout Europe."
The Turkish side visit Meadow Lane on Tuesday July 16 in a 7.30pm kick-off, while the Vallecano match is on Tuesday July 23.
Their match against Romanian champions Steaua will take place at St George's Park in Burton on July 2.