The game will take take place on Saturday March 7, with a 5.45pm kick-off, and will be broadcast live on BBC One and TNT Sports.
Full ticket information will be released in due course.
With Wrexham on FA Cup duty that weekend after beating Ipswich Town 1-0 to secure their place in the last 16 of the competition for the first time in 29 years, the Championship fixture away to Watford will have to be rearranged.
With the date confirmed for the game against Chelsea, the home league match with Hull City remains unchanged on Tuesday March 10 with a 7:45pm kick-off, and the Welsh derby against Swansea City - also at The Racecourse - is also unchanged on Friday March 13 with a 8pm kick-off.
Prior to beating Ipswich, who head to north Wales for a big league game on Saturday, Wrexham beat Premier League strugglers Nottingham Forest on penalties in round three after drawing 3-3.
Wrexham are currently seventh in the second tier, only out of the play-off places on goal difference.