Councillor Morgan led Labour to victory in the local elections last Thursday (7 May), taking the most seats – 23 out of 54 – although short of a majority.
He will lead a minority administration with the same two deputies as before the election, Councillor Gill Mitchell and Councillor Les Hamilton.
They are among the eight Labour councillors to have held their seats.
One of the 15 new councillors, Maggie Barradell, has been chosen as the Labour group’s chief whip. She is the wife of former council chief executive John Barradell and, like Councillor Morgan and Councillor Mitchell, represents the East Brighton ward.
Councillor Morgan is expected to select colleagues to chair committees such as planning, licensing and children and young people within the next week.
All the posts will be ratified at the annual council meeting on Thursday 21 May.