The Danish playmaker has joined United on a three-year deal.
Russian owner Roman Abramovich put the club up for sale in early March following Russia's invasion of Ukraine.
Timo Werner and Mason Mount scored two goals each in the 6-0 win.
Abramovich has said that he “will not be asking for any loans to be repaid” by the club.
Manchester United drew 1-1 with Southampton in the English Premier League on Saturday.
Salah's Liverpool teammate Sadio Mane led Senegal to their first ever Africa Cup of Nations title on Sunday.
Klopp's team posted 3-1 win over Crystal Palace.
Minamino came off the bench to score in a 3-0 win for Jurgen Klopp's side.
Rangnick steps in to replace Solskjaer, who was removed after United's 4-1 defeat by Watford this month.
It was ultimately a disappointing derby with City's superiority in all areas confirmed abundantly while Ole Gunnar Solskjaer's showed once again they simply lack enough quality to mount even a token title bid.