Sanchez spent nearly four years at Arsenal after a 35 million euro transfer from Barcelona in 2014.
He helped them to two FA Cups and three Community Shield titles. The 29-year-old will start his life as a United player in the squad for Friday's fourth round FA Cup tie at fourth division Yeovil.
"We've got one of the best attacking players in the world. I think he'll be very important for us because we want to have the best players possible," Mourinho said ahead of the clash.
"Alexis is a player that becomes more than a player because of his multi-functionality. I say he can play in four different positions in attack."
Earlier this week Yeovil reacted to Sanchez's potential debut with a cheeky tweet. "You said you've joined 'the biggest club in the world @Alexis_Sanchez so it's only right you start your #MUFC career in the biggest away dressing room in @SkyBetLeagueTwo. Maybe."
The top four clubs in the Premier League will be in action over the weekend. Manchester City play at second tier Cardiff City on Sunday and Chelsea, last season's beaten finalists at Wembley, host fellow Premier League outfit Newcastle United. Liverpool, who are fourth in the top flight, take on West Brom.
Manchester City have already booked a date at Wembley. They will appear in the final of the League Cup on 25 February against Arsenal.
Manchester City boss Pep Guardiola, who will use the occasion to try to win his first piece of silverware at City, said: "I like the Premier League a lot because every single weekend or every three days you have to be ready. For me that is more important. The Champions League is the most beautiful, the most prestigious.
"But the Premier League is something special -- like it was the La Liga for me or the Bundesliga in Germany. After that the FA Cup is important, and now we are in the final of the League Cup we try to win that."