The move will allow for greater collaboration and alignment on commercial priorities and the brands' games roadmap, among other things.
Hamilton will, in addition to the role as COO of NetEnt Group, also remain as CEO of Red Tiger.
Therese Hillman, CEO of NetEnt Group, said: "The acquisition of Red Tiger has proven to present even greater potential than we expected, and we would like to initiate a full integration sooner, rather than later.
"Having a Group COO is key for us moving towards full integration and to capitalise on all opportunities. For this role I can think of no one better than Gavin."
Hamilton said: "I am extremely excited to take on this role. Our success in the coming years will be determined by the decisions we make now on how we most effectively leverage our scale, people and technology.
"Closer collaboration will allow us to address the issues we face in increasing regulation and taxes in our core markets and will position us more effectively to take advantage of growth in new markets."
