It's a reverse of the 2001/02 First Round tie which resulted in Brian Little's Tigers winning 3-2 at the Racecourse Ground thanks to goals from Theodore Whitmore, Mark Greaves and Gary Alexander. It's the only win for City since the Division Two victory in 1995 when Rob Dewhurst, Gary Lund and Dean Windass were on target in a 3-2 victory. Since then, the Dragons have knocked City out of both the FA Cup in 1995/96 and the Auto Windscreens Shield in 1998/99, as well as denying City in four league meetings.
Former Hull City trainee Matt Baker will probably be in goal for Wrexham, having just signed for them from Hereford. Baker, now 24, played 4 times for City before leaving in 2000.
Elsewhere in this morning's draw, Scunthorpe go to Nottingham Forest, Grimsby host Wigan, and Huddersfield got the game they wanted with a trip to Leeds United.
The First Round winners go through to Round Two when most of the Premiership sides enter the competition, to be played on 21st/22nd September.
Today's draw in full:
Sunderland v Chester City
Darlington v Barnsley
Hull City v Wrexham
Nottingham Forest v Scunthorpe United
Rochdale v Wolves
Bradford City v Notts County
Bury v Burnley
Tranmere Rovers v Shrewsbury Town
Crewe Alexandra v Blackpool
Mansfield Town v Preston North End
Sheffield Wednesday v Walsall
Sheffield United v Stockport County
Hartlepool United v Macclesfield Town
Doncaster Rovers v Port Vale
Oldham Athletic v Stoke City
Grimsby Town v Wigan Athletic
Rotherham United v Chesterfield
Leeds United v Huddersfield Town
Colchester United v Cheltenham Town
Peterborough United v Milton Keynes Dons
Gillingham v Northampton Town
Brighton & Hove Albion v Bristol Rovers
Leyton Orient v Bournemouth
Wycombe Wanderers v Bristol City
Boston United v Luton Town
Watford v Cambridge United
Queens Park Rangers v Swansea City
Kidderminster Harriers v Cardiff City
West Ham United v Southend United
Ipswich Town v Brentford
Rushden & Diamonds v Swindon Town
Oxford United v Reading
Yeovil Town v Plymouth Argyle
Coventry City v Torquay United