Albion will welcome Sheffield Wednesday, who are ninth in the Championship, to the Amex Stadium in a tie to be played over the first weekend in January.
Brighton last played Wednesday in the FA Cup in 1983 when they beat them 2-1 in the semi-final played at Highbury.
Albion went on to the final at Wembley and drew 2-2 with Manchester United but lost out 4-0 in the replay.
Last season Brighton enjoyed a run to the FA Cup semi-final but were narrowly beaten 1-0 by Manchester City at Wembley.
Albion travel to Arsenal on Thursday in the Premier League. They also face Wolves, Crystal Palace, Sheffield United, Tottenham, Bournemouth, and Chelsea in the Premier League before their cup clash with Garry Monk's Sheffield Wednesday.
FA Cup third round draw in full
Leicester City v Wigan Athletic
QPR v Swansea City
Fulham v Aston Villa
Chelsea v Nottingham Forest
Wolves v Manchester United
Charlton Athletic v West Brom
Rochdale or Boston United v Newcastle United
Cardiff City v Forest Green Rovers or Carlisle United
Oxford United v Exeter City or Hartlepool United
Sheffield United v AFC Fylde
Southampton v Huddersfield Town
Liverpool v Everton
Bristol City v Shrewsbury Town
Bournemouth v Luton Town
Brighton v Sheffield Wednesday
Bristol Rovers or Plymouth Argyle v Coventry City or Ipswich Town
Eastleigh or Crewe Alexandra v Barnsley
Manchester City v Port Vale
Middlesbrough v Tottenham
Reading v Blackpool
Watford v Tranmere Rovers
Preston v Norwich City
Millwall v Newport County
Crystal Palace v Derby County
Solihull Moors or Rotherham United v Hull City
Brentford v Stoke City
Fleetwood Town v Portsmouth
Arsenal v Leeds United
Gillingham v West Ham United
Burton Albion v Northampton Town
Burnley v Peterborough United
Birmingham City v Blackburn Rovers