The Spain midfielder completed his £37.1million move from Chelsea on Saturday and is expected to go straight into the starting line-up on Tuesday.
Mata's arrival is a timely boost for United, who crashed out of the League Cup on penalties in their semi-final against Sunderland last week on the back of a 3-0 top-flight defeat at Chelsea.
Manager David Moyes will be expecting Mata to provide the touch of class that United have been lacking in what has been a disappointing season so far for the Premier League champions.
United's prospects of retaining their title are forlorn, as Moyes' men are seventh in the table and 14 points adrift of leaders Arsenal.
Moyes will still be confident of clinching qualification for the UEFA Champions League, though, as Liverpool are six points better off than the Old Trafford outfit.
United drew 2-2 at Cardiff back in November in the first meeting between the two sides since 1975 and since then Solskjaer replaced Malky Mackay at the Welsh club.
The 40-year-old can expect a rapturous reception on his return to Old Trafford, where he spent 11 years during his playing days and enjoyed a major role in such a successful period in United's history, including scoring the winner in the 1999 Champions League final.
The Norwegian has been charged with the task of keeping Cardiff in the Premier League, but they slipped to the bottom of the table with a 4-2 defeat at Manchester City in their last top-flight match.
Cardiff need to improve their away form if they are to avoid a return to the Championship, as they have won only once on their travels in the top flight.
Solskjaer's side did win at Bolton Wanderers in the fourth round of the FA Cup on Saturday, but Cardiff have taken just a point from their last six Premier League games.
The Cardiff boss will be hoping United strike duo Robin van Persie (thigh) and Wayne Rooney (groin) are not yet ready to return.
Moyes will also assess the fitness of Rio Ferdinand (knee), Nani (hamstring) and Michael Carrick (ankle), but captain Nemanja Vidic will not definitely not feature as he serves the second of a two-match suspension following his red card at Chelsea.
Kenwyne Jones could make his Cardiff debut if a swap deal with Stoke City involving Peter Odemwingie goes through in time and forward Jo Inge Berget could make his bow following his move from Molde last week.
The likes of Fraizer Campbell, Steven Caulker and Craig Noone are expected to return to the starting line-up.
