PSG host relegation battling Le Havre on Saturday
The former Paris St Germain player had revealed on social media on Thursday that he was Old Trafford-bound, but United had not confirmed the signing.
"Zlatan needs no introduction. The statistics speak for themselves," new United manager Jose Mourinho said in a club statement.
"Ibra is one of the best strikers in the world and a player who always gives 100 percent."
Details of the 34-year-old's contract were not disclosed.