The FA Cup fourth-round tie between Cambridge United and Manchester United will be screened live on BBC One.
The League Two side will host Louis van Gaal's Premier League giants on Friday, 23 January with a 19:55 GMT kick-off.
The sides have not met since a League Cup tie in October 1991, which the top-flight side won 4-1 on aggregate.
The BBC will also broadcast Bristol City v West Ham on Sunday, 25 January, a 14:00 GMT kick-off after the teams won their third-round replays.
Manchester United, who have lifted the trophy 11 times, last won it in 2004.
BBC Wales will screen the match between Swansea and Blackburn Rovers, which is a 12:45 GMT kick-off on Saturday, 24 January.
In addition to the fourth-round coverage, the third-round replay between Championship side Ipswich Town and the Premier League's Southampton is live on BBC One.
Ipswich earned a replay with Ronald Koeman's side following a 1-1 draw at St Mary's on Sunday.
The match will take place on Wednesday, 14 January at Portman Road, with kick-off at 19:55 GMT.
The winners will host Crystal Palace in the fourth round on 24 or 25 January.
|FA Cup fourth-round draw|
|Southampton or Ipswich Town v Crystal Palace||Cambridge United v Manchester United|
|Blackburn Rovers v Swansea City||Chelsea v Millwall or Bradford City|
|Derby County v Chesterfield||Preston NE v Sheffield United|
|Birmingham City v West Brom||Aston Villa v AFC Bournemouth|
|Cardiff City v Reading||Liverpool v Bolton Wanderers|
|Burnley or Tottenham v Leicester City||Brighton & HA v Arsenal|
|Rochdale v Stoke City||Sunderland v Fulham|
|Bristol City v West Ham||Manchester City v Middlesbrough|