In another eagerly anticipated matchup, Manchester United will face off with Steven Gerrard's Aston Villa. There will also be a rematch between Leeds United and Wolves following the teams' clash on the opening weekend of the Premier League season that featured a heated exchange between managers Jesse Marsch and Bruno Lage.
The third round matches will take place between Nov. 8 and Nov. 10.
On Wednesday, Premier League clubs Newcastle United and Leeds United overcame lower division opposition to secure their places in the third round.
Newcastle had to fight back from a goal down to beat League Two Tranmere Rovers who had taken the lead through a 24th-minute Elliott Nevitt finish.
Jamaal Lascelles brought Eddie Howe's side level with a close-range drive before the interval and New Zealand striker Chris Wood glanced in a superbly delivered corner from Kieran Trippier to secure a 2-1 win in the 52nd minute.
Leeds also had a scare before running out 3-1 winners over Yorkshire neighbours Barnsley.
A Louis Sinisterra strike from 20 metres put Leeds on their way before Mateusz Klich doubled the advantage from the penalty spot.
A diving header from Mads Andersen gave Barnsley hope and they could have drawn level from the penalty spot but Callum Styles hit the post.
Klich made sure of the win with a curling shot in the 56th minute.
Premier League Brighton & Hove Albion cruised to a 3-0 win at League One Forest Green Rovers while Championship (second tier) Bristol City won 3-1 at League One Wycombe Wanderers.
The biggest upset in the second round came on Tuesday when Premier League Fulham went down 2-0 at the hands of fourth-tier Crawley Town.
Manager Marco Silva made 10 changes for the trip and Crawley took advantage when Tom Nichols slotted a 16th-minute opener.
Liverpool loanee James Balagizi made it 2-0 shortly after half-time and the hosts held on comfortably to prompt a pitch invasion after the final whistle.
Full draw as follows:
Leicester City vs. Newport County
Wolves vs. Leeds
Nottingham Forest vs. Tottenham
West Ham vs. Blackburn
Manchester United vs. Aston Villa
Bournemouth vs. Everton
Liverpool vs. Derby County
Burnley vs. Crawley Town
Bristol City vs. Lincoln City
Manchester City vs. Chelsea
Stevenage vs. Charlton
MK Dons vs. Morecambe
Newcastle vs. Crystal Palace
Southampton vs. Sheffield Wednesday
Arsenal vs. Brighton
Brentford vs. Gillingham
Information from Reuters was used in this report