The Minstermen, promoted from the BlueSquare Premier courtesy of a play-off final triumph over Luton Town, travel to the Keepmoat Stadium as Hull City were handed an all-Yorkshire first round clash at home to Rotherham United.
Keith Hill was another happy with the draw for the Capital One Cup after his Barnsley side were drawn away at Rochdale, the club he led to promotion from League Two in 2010.
Elsewhere, Leeds United host Shrewsbury Town as newly-promoted Huddersfield Town travel to Preston North End while Sheffeld Wednesday are also on the road after being handed a visit to Oldham Athletic.
Steel City rivals United will host Burton Albion as Bradford City travel to Notts County and Middlesbrough go to Bury.
The ties will be played in the week beginning August 13, unless both clubs agree to the tie taking place on either the Saturday or Sunday. The League season will then kick off on August 18.
Full draw: Port Vale v Burnley, Derby v Scunthorpe, Rochdale v Barnsley, Notts County v Bradford, Hull v Rotherham, Fleetwood v Nottingham Forest, Carlisle v Accrington, Doncaster v York, Crewe v Hartlepool, Bury v Middlesbrough, Chesterfield v Tranmere, Sheffield United v Burton, Blackpool v Morecambe, Leeds v Shrewsbury, Preston v Huddersfield, Oldham v Sheffield Wednesday, Cheltenham v Milton Keynes Dons, Ipswich v Bristol Rovers, Stevenage v AFC Wimbledon, Exeter v Crystal Palace, Yeovil v Colchester, Birmingham v Barnet, Bristol City v Gillingham, Northampton v Cardiff, Plymouth v Portsmouth, Wolves v Aldershot, Walsall v Brentford, Millwall v Crawley, Torquay v Leicester, Dagenham v Coventry, Peterborough v Southend, Swindon v Brighton, Watford v Wycombe, Charlton v Leyton Orient, Oxford v Bournemouth.