Zynga also plans to buy the remaining 20% in equal installments over the following three years, it said in a statement on Wednesday.
The US firm expects to finalise the takeover of the 80% interest in Rollic on October 1.
Through the transaction, Zynga is entering the so called hyper-casual market of easy-to-play mobile games. The acquisition is also expected to increase Zynga's audience and grow its advertising business, the buyer said.
Established in 2018, Rollic has titles with over 5 million mobile daily active users and 65 million mobile monthly active users in total.
In June, Zynga said it has agreed to buy Turkish mobile gaming company Peak in a cash-and-stock deal worth $1.8 billion.
($ = 0.8442 euro)