The deal is worth $5.9bn (£3.8bn), reports The BBC.
Activision said in a statement the acquisition would make it a global leader in interactive entertainment across mobile, console and PC platforms.
The Call of Duty series is one of the world’s best selling console games.
Candy Crush is among the most popular games on mobile devices.
Video game publishers are switching from the physical sale of games to digital growth as consumers move from consoles to playing on smartphones and tablets.
Activision Blizzard’s chief executive Bobby Kotick told the Reuters news agency that the company wanted to broaden its reach and appeal to a larger demographic.
He said that 60 per cent of King Digital Entertainment’s players were female, and that no games console or hardware, besides a smartphone, was needed to access its games.
