Johnson was born in the south-west area of London and grew up living opposite Craven Cottage, and he will now return there with his Posh side over the weekend of January 8/9.
He told United`s official website: "Personally, this is a great draw for me. I was born in Fulham and the ground was literally across the road from me so I supported the club and I`m looking forward to taking Peterborough United there in the new year.
"It is obviously pleasing to get a Premier League club after negotiating two tricky first and second-round ties. I`m sure we`ll take a large following of supporters, it is not too far to travel and the stadium can create a very good atmosphere.
"Obviously we have a lot of league games between now and then to concentrate on, but it is a tie we can certainly look forward to."
Peterborough`s scheduled League One fixture against Brentford on Saturday January 8 will now be moved, with no new date yet arranged for the London Road fixture.
Source: PA
Source: PA