The game is to be played on Sunday 5 January, kicking off at the unusual time of 6:16pm and being broadcasted live on BT Sport.
Every third round tie will kick off a minute later to encourage fans to ‘Take A Minute’ to think about looking after their mental health.
Gillingham advances to the next round after beating Doncaster 3-0 at Priestfield Stadium on Sunday.
Gillingham made a great start to the match, scoring two goals in the opening 15 minutes, Mark Bryne scored first on the 11th minute with Olly Lee scoring four minutes later to make it 2-0 as the clock hit 15 minutes. Brandon Hanlan confirmed Gillingham’s progression to the next round as he scored the third and final goal of the game to end the match 3-0.
The Gillingham manager, Steve Evans shared his thoughts after the draw, “I wanted West Ham. It’s a fantastic club with brilliant supporters and owners who I know well. I have the utmost respect for Manuel Pellegrini, and it will be great to see him again.”