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 BBC will bring you all the best live action, highlights and analysis all the way to Wembley.
The first-round action kicks off on the Friday with live coverage from one of the most anticipated ties on BBC Two at 19:30 GMT, presented by Dan Walker along with Trevor Sinclair and Jermaine Jenas.
On Saturday, 7 November Football Focus will be live from 12:10 at one of the day's big fixtures, with FA Cup Final Score showing all the key action as it happens from eight selected matches on Sunday, 8 November.
Every goal from every match will be available on the BBC Sport website and app as part of the BBC's extensive digital coverage, providing fans with action as early as 17:15 on the Saturday.
Finally, there will also be a comprehensive 90-minute highlights show on BBC Two on the Sunday at 18:30.
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 v Boreham Wood
Coventry City v Northampton Town
Brackley Town v Newport County AFC
Grimsby Town v St Albans City
Hartlepool United v 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 v Welling
FC Halifax v Wycombe Wanderers
Crawley Town v Luton Town
Doncaster Rovers v Stalybridge
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 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