Didcot, the lowest-ranked team in the FA Cup, will play League Two’s Exeter City at home in the first round proper.
The Oxfordshire outfit play in the Southern Division One South & West, the eighth tier of English football.
Wigan, who won the cup in 2013, travel to fellow League One side Bury while 2008 winners Portsmouth will host Macclesfield Town.
Thirty-two non-league sides join 48 league clubs in the round, with ties beginning on Friday, 6 November.
Among the other eye-catching ties, last season’s quarter-finalists Bradford City of League One travel to National League outfit Aldershot.
Meanwhile Northern Premier League Premier Division side Salford City, who are part-owned by five former Manchester United players, will face League Two side Notts County.
The FA Cup first round draw in full:
Burton Albion v Peterborough United
Port Vale v Maidenhead United
Barnet v Blackpool
Bristol Rovers v Chesham United
Cambridge United v Basingstoke Town
Mansfield Town v Oldham Athletic
Altrincham v Barnsley
Crewe Alexandra v Eastleigh
Northwich Victoria or Chorley v Boreham Wood
Coventry City v Northampton Town
Brackley Town v Newport County AFC
Grimsby Town v St Albans City
Hartlepool United v Havant and Waterlooville or Cheltenham Town
Salford City v Notts County
Dover Athletic v Stourbridge
Stevenage v Gillingham
Millwall v AFC Fylde
Aldershot Town v Bradford City
Walsall v Fleetwood Town
Bury v Wigan Athletic
Portsmouth v Macclesfield Town
Sheffield United v Worcester City
Barwell or AFC Rushden & Diamonds v Grays Athletic or Welling
FC Halifax or Guiseley v Wycombe Wanderers
Crawley Town v Luton Town
Doncaster Rovers v Stalybridge or North Ferriby United
Didcot Town v Exeter City
Dagenham & Redbridge v Morecambe
Leyton Orient v Staines Town
Gainsborough Trinity v Shrewsbury Town
Maidstone United v Yeovil Town
Braintree Town v Oxford United
Whitehawk v Tranmere Rovers or Lincoln City
Accrington Stanley v York City
Scunthorpe United v Southend United
AFC Wimbledon v Forest Green Rovers
Plymouth Argyle v Carlisle United
FC United of Manchester v Chesterfield
Rochdale AFC v Swindon Town
Wealdstone v Colchester United