Albion's Carabao Cup journey will begin with a second round clash at The Hawthorns against Arsenal.
The fixture will be played on the week commencing Monday, August 23.
The two sides last met in May, with Arsenal winning 3-1 at the Emirates. The Gunners also won the reverse fixture in January, but Albion have beaten the London side on home turf as recently as March 2017.
Further details on the Baggies' fixture against Arsenal will be released in due course.
See the full Carabao Cup second round draw below:
Northern section
Oldham Athletic v Accrington Stanley
Newcastle United v Burnley
Wigan Athletic v Bolton Wanderers
Huddersfield Town v Everton
Sheffield United v Derby County
Stoke City v Doncaster Rovers
Shrewsbury Town v Rochdale
Nottingham Forest v Wolves
Morecambe v Preston North End
Blackpool v Sunderland
Leeds United v Crewe Alexandra
Barrow v Aston Villa
Southern section
Brentford v Forest Green Rovers
Millwall v Cambridge United
West Bromwich Albion v Arsenal
Norwich City v AFC Bournemouth
Cardiff City v Brighton & Hove Albion
Birmingham City v Fulham
Gillingham v Cheltenham Town
Queens Park Rangers v Oxford United
Swansea City v Plymouth Argyle
Stevenage v Wycombe Wanderers
Newport County v Southampton
Northampton Town v AFC Wimbledon
Watford v Crystal Palace