Gary Rowett's Stoke were relegated from the Premier League last season.
Also tackling Premier League opposition in the Cup will be Barnsley, who travel to Burnley.
Here at The Sportsman we will be keeping you bang up-to-date with all the action, as a couple of former winners of the prestigious cup competition, Ruud Gullit and Paul Ince, pluck each of the 64 balls out of the tub, alongside host Mark Chapman.
Doncaster Rovers travel to Preston North End, while both Sheffield clubs have been drawn at home.
Woking, one of two non-league sides guaranteed to be in the third round, will host Premier League team Watford.More news: Michigan Wolverines Football To Face Florida In The Peach Bowl
Shrewsbury, who have appointed Sam Ricketts as boss, have seen off Salford City and Scunthorpe United to reach the third round stage for the fifth time in 23 attempts.
Tottenham haven't won a trophy since lifting the League Cup in 2008 and haven't won the FA Cup since 1991 so Mauricio Pochettino will be desperate to try and go all the way this season.
Traditionally one of the biggest moments of the football season, the draw for the FA Cup third round takes place on Monday evening.
The 3rd round ties will be played the week commencing the 5th January 2019.