The tie will take place over the weekend of January 8-10, potentially in-between an EFL Cup semi-final for the Blues on January 4/5 and the trip to Wolves in the Premier League on January 12.
Last time they met was in the 2018-19 Carabao Cup, when Marco Silva’s Toffees ran out 3-1 winners at Goodison Park in August 2018, with Dominic Calvert-Lewin netting a brace.
Paul Warne’s side are currently 19th in the Championship with three wins from their 14 games so far this season.
Everton have won the competition five times in their 142-year history, but their FA Cup triumph over Manchester United in 1995 remains their most recent piece of silverware.
They reached the semi-finals in 2016, but have not made it past the fourth round in the four years since, suffering defeats to Liverpool (twice), Leicester City and Millwall.
FA Cup: Full Third Round Draw:
Huddersfield Town vs Plymouth Argyle
Southampton vs Shrewsbury Town
Chorley vs Derby County
Marine vs Tottenham
Wolverhampton Wanderers vs Crystal Palace
Stockport County vs West Ham United
Oldham Athletic vs AFC Bournemouth
Manchester United vs Watford
Stevenage vs Swansea City
Everton vs Rotherham United
Nottingham Forest vs Cardiff City
Arsenal vs Newcastle United
Barnsley vs Tranmere Rovers
Bristol Rovers vs Sheffield United
Canvey Island/Boreham Wood vs Millwall
Blackburn Rovers vs Doncaster Rovers
Stoke City vs Leicester City
Wycombe Wanderers vs Preston North End
Crawley Town vs Leeds United
Burnley vs Milton Keynes Dons
Bristol City vs Portsmouth
Queens Park Rangers vs Fulham
Aston Villa vs Liverpool
Brentford vs Middlesbrough
Manchester City vs Birmingham City
Luton Town vs Reading
Chelsea vs Morecambe
Exeter City vs Sheffield Wednesday
Norwich City vs Coventry City
Blackpool vs West Bromwich Albion
Newport County vs Brighton and Hove Albion
Cheltenham Town vs Mansfield Town
Ties to be played over weekend of January 8-10