The Gunners held their nerve to beat West Brom on penalties with Chelsea coming through 2-0 victors against Swindon.
Two-time winners Manchester City, who dispatched Wigan with a 5-0 win at the Etihad Stadium on Tuesday night, have been drawn away against Newcastle.
The fourth-round ties will be played the week commencing October 28.
Full fourth-round draw
Birmingham City v Stoke City
Manchester United v Norwich City
Arsenal v Chelsea
Tottenham Hotspur v Hull City
Newcastle United v Manchester City
- Sports & Recreation
- Manchester City
- Hull City
- Manchester United