Mourinho confirmed United have broken their transfer record - a £30.75million deal for Dimitar Berbatov in 2008 - to recruit the 25-year-old, who was Chelsea's player of the year in each of the last two seasons.
The Chelsea boss said: "Things are going in a good direction and we allowed Juan to travel and to have the medical with United. I think at Manchester.
"Things are really going in that direction. Sooner, rather than later, things will be finalised.
"He's a fantastic player and despite not playing a lot for us in the last period could be a very important player for us. But Juan had this fantastic opportunity for him.
"It's what he wants. 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.
"It's good for Juan, it's good for the Premier League and the offer in financial terms, is the right offer.
"The offer, compared with what the club paid two years ago (when Mata signed from Valencia), was fantastic.
"If Man United pays 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 and we hope that he does very well for them. No fears at all. We are convinced he's going to do well.
"When we play him we are going to try to win and he does the same."
Some commentators have suggested Mourinho is no longer concerned by Manchester United after selling to a long-standing direct rival, who are 14 points adrift in the title race.
Mourinho added: "We are not afraid of him going there to do very well for Man United. We want him to go there, to do well for Man United."
Arsenal boss Arsene Wenger suggested the transfer was unfair, as Chelsea have already played United twice this season and will not have to face Mata this term, where other title contenders will.
Mourinho added: "Wenger complaining is normal, because he always does. It's something that we know.
"When a player plays for a club on August 20 and two weeks later on September 5 plays against the same club with a different shirt, this is normal, because this is the market.
"We don't do the market, we don't do the rules, we have just to do according to the rules.
"If Wenger sells (Mesut) Ozil to Man United in this moment I would be very happy because he sells a very important player.
"Normally he should be happy that Chelsea sold a player like Juan Mata, but this is a little bit his nature.
"When he says this is not fair, I think what is not fair is that his team always has the best days to play."
Mourinho and Chelsea moved quickly to replace Mata with Mohamed Salah after reaching an agreement with Basle, subject to personal terms and a medical.
"It was a surprise for us that Juan was leaving," Mourinho said.
"We were not prepared to make a bid or to try to bring a player to replace Juan in the squad so everything happened very, very fast.
"We decided to try to go for Salah. We started from zero; no contacts with the club, no contacts with the player.
"The first step was an agreement with the club. That situation is done, no more discussions, everything is signed and done subject to the medical, that we didn't have yet and subject to the player's desire to join us or not.
"Now we know he wants (to come)."
Mourinho has spoken to Salah, who was also interesting Liverpool.
Liverpool manager Brendan Rodgers has not given up hope and Mourinho admits a last-minute U-turn is feasible, although the Egypt winger's preferred destination is west London.
Mourinho said: "We know that the player wants to come. He told me personally.
"Now it's (personal) terms, the medical that he has to pass probably in Zurich or Lausanne and hopefully he comes.
"Probably the situation is still open and not closed."
Salah is set to become the third signing of the winter transfer window, following the captures of Bertrand Traore and Nemanja Matic.
Kevin De Bruyne has already left for Wolfsburg, Mata is en route to Manchester and Michael Essien has permission to leave, too.
"Michael Essien is in this moment in a position where he can go or he can stay," Mourinho said.
"If he stays we are more than happy for him to stay, but he's another player that gave everything to this club and if a great situation for him arrives for his future... we must show him respect.
"If he stays, he stays and if he stays he's playing against Stoke."
Chelsea play Stoke on Sunday in the FA Cup fourth round, with striker Fernando Torres (knee) missing for three weeks.