Undoubtedly the tie of the last 16, it had looked like it would not come to fruition as the Gunners struggled at the Hawthorns.
However, with the match ending 1-1 after extra time, Arsene Wenger's side eventually won 4-3 on penalties to secure a home tie with Jose Mourinho's Chelsea on either October 29 or 30.
Wenger said: "It will be an interesting game. They have a very large squad so we will know we are playing another Premier League team, and on our side, we are at home. So it will be interesting."
Arsenal v Chelsea is one of five all-Premier League encounters in the last 16.
Newcastle will welcome Manchester City to St James' Park after overcoming Leeds, while Hull travel to Tottenham just days after heading to White Hart Lane in the Premier League.
Managerless Sunderland play host to Mauricio Pochettino's Southampton, while Manchester United's reward for beating rivals Liverpool is a home clash with Norwich.
"Well, you always want a home draw if you can get it," United boss David Moyes told Sky Sports 1.
"Norwich are a good side, they have got a good manager and we will give them every respect."
Elsewhere, West Ham head north to take on Sky Bet Championship outfit Burnley and Martin Jol's Fulham travel to Leicester in search of a quarter-final berth.
Birmingham ousted holders Swansea 3-1 and have been handed another home match in the last 16, this time against Mark Hughes' Stoke.