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Welling will play Carlisle in the second round of the FA Cup following the draw on Monday evening.
The Wings will have home advantage with the game being played at Park View Road. Carlisle are eighth in League 2 with 26 points from 17 games and had an impressive first-round win at Plymouth to reach this stage.
Welling boss Loui Fazakerley said: "It's great to finally have a home draw.
"We were due a bigger club though as we've had some pretty favourable draws in the last two rounds.
"Hopefully we can get all the locals up for it and sell the game out. We have got more than enough motivation and quality in our squad to win the game."
Welling reached this stage after winning 2-0 at Northern League Premier Division Barwell on Saturday thanks to goals from captain Ricky Wellard and Michael Bakare.
It is the second time in three years that the Wings have reached this stage. Under Jamie Day they beat Brislington and Luton before bowing out 3-1 at Plymouth in 2013/14.
This is Fazakerley's first experience of the FA Cup as a manager as he only took charge of the Wings in March.
The game is due to take place on the weekend of Saturday, December 5.