The 53-year-old replaces Louis van Gaal who was sacked on Monday, two days after his side won the FA Cup, United's first trophy in three years.
Ferdinand, who won six Premier League trophies with the club, said Mourinho would have to teach the team how to start winning again after the club missed out on Champions League football for the second time in three years.
“This is Jose Mourinho's most exciting and most challenging job yet,” the former England centre half wrote on his Facebook page.
“The first thing he needs to do is instil a 'winning mentality' back into the club. One thing I can tell Manchester United fans is that they have got themselves a true winner in all aspects. His CV shows success.”
Ferdinand said Mourinho would be motivated by the desire to prove his critics wrong after a disappointing title defence with Chelsea that led to him being sacked in December.
“After his recent unsuccessful time at Chelsea in the final year, I can assure you this winner is now a wounded animal which makes him such a mouth-watering appointment,” added the former Leeds United, West Ham United and Queens Park Rangers defender.
“He will be desperate to silence the media who have been writing and saying negative things about him and will be as focused as ever.”
Original source: Ferdinand welcomes Mourinho to United