The Barclays Premier League duo drew 2-2 last Sunday, resulting in a replay.
The winners of the Stamford Bridge contest will play Manchester City in the semi-final.
A FA statement read: "Following consultation with all relevant stakeholders, The FA can confirm that The FA Cup with Budweiser Sixth Round Proper Replay between Chelsea and Manchester United at Stamford Bridge will take place on Easter Monday 1 April, live on ITV. Kick-off is at 12.30pm."
The decision means Chelsea's Barclays Premier League fixture with Southampton, which had been due to take place on Easter Sunday, will now take place a day earlier and with a 3pm kick-off.
Finding a suitable date for the fixture proved challenging due to Chelsea's involvement in the Europa League and the confirmed FA Cup semi-final dates of April 13 and 14.
It had been expected the FA would wait to see if Chelsea advance in the Europa League Thursday before determining a date.
They must overturn a 1-0 first-leg deficit to the Romanians to reach the Europa League quarter-finals.
The rescheduling means Chelsea and Manchester United, who visit Sunderland on March 30, play their Premier League matches on the same day, but has irked Southampton.
A statement on Southampton's official website read: "The game had already been moved once for the purposes of live Sky TV coverage - to Sunday, March 31 - however, the Premier League have deemed it acceptable to move the fixture once more.
"The club is extremely disappointed that this decision has been taken; not least because of the significant inconvenience a second change to the fixture will cause our supporters."
Chelsea's upcoming fixtures:
March 14 (h) vs Steaua Bucharest (Europa League)
March 17 (h) vs West Ham (Premier League)
March 18-27 International break
March 30 (a) vs Southampton (Premier League)
April 1 (h) vs Manchester United (FA Cup quarter-final replay)
April 4 (TBC) Europa League quarter-final first leg.
April 6/7 (h) vs Sunderland (Premier League)
April 11 (TBC) Europa League quarter-final second leg.
April 13 & 14 FA Cup semi-final weekend.