Moro, 22, has signed a five-year deal with the Russian club for an undisclosed fee.
Transfer Nexus reported exclusively on advanced talks between the sides earlier this month, and the final details have since been sorted.
Moro has been compared to his countryman Luka Modric and a move from Croatia to Russia is an important step in his career.
Several European clubs wanted to sign Moro this summer, but in the end he chose the Muscovites.
The central midfielder will wear the number eight shirt at Dynamo.
А мы знаем. Добро пожаловать, Никола! 👋 pic.twitter.com/xIx6I6fLaa
— ФК «Динамо» Москва (@FCDM_official) August 17, 2020