The tie will take place on the first weekend of November. It's the second time in two seasons Boro have made it this far in the FA Cup.
Boro may fancy their chances, as Burton are without a win in the league so far this season.
The fixture will see Scarborough Athletic face their highest placed opponents in a competitive fixture since the new club was formed.
Boro's journey to the First Round proper began with a replay victory over Dunston Town in the 2nd Qualifying Round, before a win away at Warrington Rylands.
Two days ago, Scarborough put in a superb performance to beat National League North rivals Chester 3-1 and in doing so set up this mouth-watering First Round clash against a side three divisions higher.
Scarborough have already made £18,375 from their FA Cup run this season and are guaranteed another £15,000, which they'll receive if they lose to.
If Boro win the tie, they'll earn an incredible £45,000 extra, taking the total to £63,375.
Last season, Scarborough reached the First Round proper for the first time since the new club was formed in 2007, going out to League Two opposition after one replay and one re-match.
The former Scarborough FC famously reached the Fourth Round when they lost 1-0 to Chelsea in 2004.
Scarborough Athletic are just two wins away from a potential clash against Premier League opposition.
Scarborough Manager Jono Greening was a guest on BBC2 during the live draw at Valley Parade and before the draw was bigging up his hometown side:
"It's a club that's on the rise, it's progressing really well. Just look at the amount of fans we have in the ground. We're on the right track".
Speaking of the draw of Burton Albion, Jono told BBC 2:
It's a really exciting time at the club, playing a team higher than us. Good challenge for the players, good challenge for the staff and we're really looking forward to it. I think it's an exciting tie for the fans"
Here's highlights from Saturday's win against Chester:
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