Verbeek stood down from the role for personal reasons after leading Oman to the knockout rounds of the Asian Cup for the first time last month.
He also led them to victory in the Gulf Cup in early 2018.
Koeman previously worked as head coach of the Hungary national team and served as an assistant coach under his brother, Ronald, during his time with English Premier League clubs Southampton and Everton.
Local media reported that the 57-year-old had been handed a two-year contract and was tasked with leading Oman to the World Cup finals for the first time in 2022. (Reuters/NAN)