United last month agreed a fee with Mexican side Guadalajara for the 22-year-old before the player also completed a medical and agreed personal terms.
United had only been awaiting confirmation of his work permit to complete his transfer, which will go through on July 1.
Hernandez's confirmation as a United player had been held up because he had played less than 75% of Mexico's internationals during the past two years.
He is, however, set to be a part of the Mexico squad at the World Cup finals in South Africa following which he is due to join United's squad for the Philadelphia leg of their pre-season tour of the United States and Canada.
Hernandez, who is nicknamed 'Chicharito', described his move to Old Trafford as "living the dream" after he completed his medical in Manchester last month.
United fans got a quick glimpse of his talents when he made a substitute appearance for Mexico against England in their 3-1 defeat at Wembley on Monday, before he scored in a 2-1 friendly loss against Holland last night.
Hernandez's signing is the first time that United have done a deal for a Mexican player.