Leeds, who knocked Manchester United out at the same stage in last season's competition before taking Tottenham to a replay in the fourth round, will be making their first trip to the Emirates Stadium over the weekend of January 8/9.
Grayson said: "It's a fantastic draw. Arsenal are one of the best teams in the country and are one of the top footballing teams in Europe. I'm sure our supporters will look forward to the game and will sell the full allocation once again.
"It's amazing when you look at the draws we've had and the performances and the support we've had. In an 18-month period we've played Liverpool, Man U, Tottenham and now Arsenal in the cups, which is fantastic for the club and the fans."