United had not been in the second-round draw of the competition for 19 years after two decades of almost unprecedented success but found themselves in the hat after failing to qualify for European competition last season.
The Dons had gone through on Tuesday evening with a 3-1 victory over fierce rivals AFC Wimbledon and will now be looking to replicate York, who eliminated United in their last second-round appearance in 1995.
"We're ecstatic, it's a dream tie for us," Robinson told mkdons.com
"After beating AFC Wimbledon last night, we are now going to be playing one of the greatest ever football teams at stadiummk, all in our anniversary season."
In Wednesday night's first-round ties, Cardiff overcame Coventry 2-1 while Sheffield United beat Mansfield by the same score
The win for the United sets up an intriguing grudge match as they travel to Upton Park to face West Ham with the Carlos Tevez affair, which some at Bramall Lane blame for their relegation in 2007, still a sour subject in South Yorkshire
Cardiff, meanwhile, will travel to face Port Vale
Last season's beaten finalists Sunderland will travel to face 2011 winners Birmingham
Gus Poyet's men lost 3-1 to Manchester City in last season's Wembley showpiece but will be confident of another cup run after last season's dramatic escape from Barclays Premier League relegation and a summer of recruitment on Wearside
League Two Burton, who created the upset of round one by beating Wigan on Tuesday night, will face even higher opposition as they welcome QPR to the east midlands.
Fulham will make the short trip to face west London rivals Brentford while Aston Villa host League One Leyton Orient.
Stoke will be heavy favourites to beat Portsmouth at the Britannia Stadium although Southampton face a potentially tougher prospect with a trip to face Millwall.
West Brom will welcome Oxford to the Hawthorns, Leicester play host to Shrewsbury and Burnley take on Sheffield Wednesday at Turf Moor.
Newcastle will face a long midweek trip as they travel to Kent to take on Gillingham while Crystal Palace head north to face off against Walsall and Swansea host Rotherham.
In the pick of the other ties, there will be a big Yorkshire derby at Valley Parade as Leeds make the short trip to face Bradford
Huddersfield face Nottingham Forest in an all-Championship affair and Middlesbrough host Preston
Watford will face Doncaster at Vicarage Road, Bournemouth will take on Northampton and Reading face a testing trip to Scunthorpe
Championship promotion favourites Derby take on Charlton, Brighton face a trip to Swindon, Bolton travel to Crewe and Norwich host Crawley
The ties will be played on August 26 and 27
Source : PA
Source: PA