The combined company "will be one of the largest pharmaceutical wholesalers and providers of logistics and services in the healthcare sector worldwide," the German firm said in a statement.
The total transaction, including McKesson's takeover of Celesio's outstanding debt is valued at approximately $8.3 billion (6.3 billion euros, the statement added.
Both firms will keep their own separate brands.
The combined firm is expected to have annual revenue of more than $150 billion, employing some 81,500 people in 20 countries worldwide.
Earlier in the month, shares in McKesson rose sharply after the Wall Street Journal reported news of the buy-out.