Cllr Osman will be formally elected as leader of the Conservative group on May 16 following Mr Maddock's announcment that he would step down last month.
Mr Maddock resigned to run for role of Avon and Somerset Police's first Crime Commissioner.
Speaking at the time, Mr Maddock said: “Deciding to stand down as Somerset County Council leader has been a really hard decision, a real wrench.
“But the new Police role is hugely important and influential. With my experience in commerce, in public service, and my contacts in local, regional and national politics, I feel I have a lot to offer.”