The draw was made at Football League headquarters this morning.
Former Leeds midfielder Terry Yorath is The Terriers assistant manager and he is delighted with the draw.
"We were looking for this fixture," he said.
"When I heard we'd drawn them I got a tingle in my body which I really enjoyed. I want to go back there and it's fantastic to get them in the cup. We get decent away support at Huddersfield and we'll take a large following with us, so we fancy our chances.
"We're a very young side at the moment and it will be a great experience for the lads. The prospect of many of our teenagers going to Elland Road will be a great incentive for them."
The game will be played on Tuesday August 24.
Full First Round Draw:
Lincoln City v Derby County
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 AFC 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