Rangers boss Stuart McCall says he feels sorry for Gael Bigirimana, but admits he should never have been signed.
Chris Gunter will stay at Reading, after the club took up the option to extend his deal by another year.
The midfielder will have a medical, almost certainly on Saturday, and personal terms are also still to be agreed.
However, unless there are any hitches, Mata will make his debut in Tuesday's Barclays Premier League encounter with Cardiff at Old Trafford.
"Manchester United is pleased to announce it has reached agreement with Chelsea Football Club for the transfer of Juan Mata for a club-record fee," said United in a statement.
"The deal is subject to a medical and the agreement of personal terms.
"A further announcement will be made in due course."
It has seemed just a matter of time before Friday night's announcement was made, with it becoming obvious Mata would be joining United as early as Tuesday.
Although manager David Moyes refused to discuss the 25-year-old following Wednesday's Capital One Cup semi-final loss to Sunderland, sources involved in the deal had confirmed it was close to being agreed.
"It's what he wants," said Mourinho.
"It's what he asked us to accept. Chelsea Football Club is proud to act this way, in an open way, in a human way.
"The offer, compared with what the club paid two years ago (when Mata signed from Valencia), was fantastic."
It is thought United have agreed to pay £37million for Mata, smashing the club record £30.75m they paid for Dimitar Berbatov in 2008.
Voted Chelsea's player of the year for the past two seasons, Mata has failed to win over Mourinho and ended up being squeezed out due to the form of Oscar and Eden Hazard.
Yet Mourinho insists the former Valencia man leaves with his best wishes.
"We hope he does well," said Mourinho. "We are convinced he is going to do well.
"If Manchester United pay their record for a player it's because they know exactly what they want.
"They are convinced he's going to be important for them.
"In spite of probably many clubs, many boards and many managers think you can't sell a top player to a rival club, especially not in the same country you play, we feel and we think differently.
"The player deserves respect, the player deserves to be happy and to play where he wants to play."
Juan Mata factfile:
1988: Born Juan Manuel Mata Garcia on April 28 in the Spanish province of Burgos.
2003: Moves from Real Oviedo's youth ranks to those of Real Madrid.
2006: July 29 - Helps Spain win the European Under-19 Championship, beating Scotland 2-1 in the final.
2007: March - Agrees a move to Valencia effective from the 2007-08 season.
June - Finishes the 2006-07 campaign with 10 goals for Real's B team, Castilla, as they are relegated from the Spanish Segunda Division.
2008: April 16 - Scores in Los Che's 3-1 win over Getafe in the Copa Del Rey final. He had also scored twice in the semi-final win over Barcelona.
2009: March 28 - Makes his senior debut for Spain as a substitute against Turkey.
May - Finishes the 2008-09 season with 11 goals and 13 assists for Valencia.
September 9 - Scores his first goal for Spain in a 3-0 win over Estonia.
2010: June - Makes one appearance in Spain's victorious World Cup campaign, as a substitute against Honduras.
2011: Helps Valencia to a second successive third-placed finish in La Liga.
June - Named as UEFA's 'Golden Player' of the European Under-21 Championship as Spain win the tournament.
August 24 - Signs for Chelsea on a five-year contract. Is given the number 10 shirt after Yossi Benayoun agrees to give it up.
August 27 - Scores on his Chelsea debut as a second-half substitute against Norwich.
September 14 - Does likewise on his Champions League debut for the club, against Bayer Leverkusen.
2012: May 5 - Named man of the match as Chelsea beat Liverpool 2-1 in the FA Cup final. Mata scored four goals and set up another four in the competition.
May 10 - Named Chelsea's fans' player of the season.
May 19 - Sets up Didier Drogba's equaliser as Chelsea win the Champions League final against Bayern Munich, despite Mata's miss in the penalty shoot-out.
July 1 - Scores the final goal as Spain beat Italy 4-0 in the final of Euro 2012.
November 6 - Named Barclays Premier League player of the month for October.
2013: March 3 - Makes his 100th Chelsea appearance in a 1-0 win over West Brom.
April 19 - Nominated for the PFA Player of the Year award, eventually won by Tottenham's Gareth Bale.
May 15 - Helps Chelsea win the Europa League, setting up Branislav Ivanovic's late winner.
May 16 - Named as Chelsea's player of the year for the second successive year, adding the players' player of the year award.
June 15 - Dismisses reports new Chelsea manager Jose Mourinho has told him he is surplus to requirements.
August 29 - Despite rarely selecting him, Mourinho insists Mata has a future at Stamford Bridge.
2014: January 17 - Rumours emerge linking Mata with a move to Manchester United.
January 22: United are reported to have tabled a £40million bid for Mata.
January 24: United reach agreement with Chelsea for transfer of Mata for a club-record fee, subject to a medical and the agreement of personal terms.