The Istanbul club announced their new signing on their website.
Besiktas will reportedly pay 3.3 million euros ($3.58 million) to Dnipro in transfer fee for the 28-year-old goalkeeper.
The Ukrainian international will be paid 4.2 million euros ($4.55 million) in total as well as 4,000 euros ($4.339) per match bonus.
Denys Boyko's former team Dnipro were the latest UEFA Europa League runners-up. Spanish team Sevilla beat them 3-2 in the final in Warsaw on May 27, 2015 as Boyko played for Dnipro.
