Steve Clarke's side follow that with a trip to Everton one week later for Roberto Martinez's first home game since succeeding David Moyes at Goodison Park.
West Brom face Premier League champions Manchester United away on 28 September, with Arsenal visiting The Hawthorns for their next fixture on 5 October.
Clarke will face former mentor Jose Mourinho at Stamford Bridge when West Brom play Chelsea in early November.
The first West Midlands derby of the Premier League season takes place when Aston Villa visit the Hawthorns on 23 November, with the return at Villa Park on 28 January 2014.
West Brom will have two trips to London over Christmas when they play Tottenham away on Boxing Day, followed by a visit to Upton Park to play West Ham on 28 December.
Stoke will be the visitors to The Hawthorns for the final game of the season on 11 May 2014.