Hogan has succeeded Jacques Rudolph as the county's four-day format skipper with the South African retiring at the end of the 2017 season.
The four-day game begins on Friday with Hogan part of an unchanged home squad.
He missed their last game, a draw against Nottinghamshire, because of shoulder and shin injuries.
Hogan has previously led Glamorgan in one Championship match, against Gloucestershire in Cardiff in 2016 when Rudolph was injured.
"I have always wanted to captain a side as my career progressed," said Hogan.
"I am not going to say that I am going to solve the world's problems but, with input from the coach and other players, I hope I can get the club moving forwards."
Glamorgan will be looking to repeat the form of their recent One-Day Cup win over Kent at the Swansea venue, after losing their Championship match there last year against Northamptonshire by 251 runs.
"It was a great day in Swansea against Kent, hopefully the pitch will be good for batting and we might see a bit of turn," said Glamorgan assistant coach David Harrison.
The two teams have not met in the Championship since 2004.
"Durham have got strong seamers, they've got an old Test player in Paul Collingwood, Keaton Jennings has done very well for them, and at England A and Test level so we'll do our homework," Harrison added.
Durham arrive after a heavy defeat by an innings and 177 runs at Sussex.
They are led by former England all-rounder Collingwood, but are without ex-England seamer Graham Onions because of a back injury.
He is replaced in the visitors' squad by fast bowler Barry McCarthy, who returns from international duties with Ireland.
Glamorgan (from): Rudolph, Selman, Bragg, Ingram, Cooke (wk), Donald, Carlson, Lloyd, Salter, De Lange, Hogan (c), Carey, Van der Gugten.
Durham (from): Paul Collingwood (c), Keaton Jennings, Stephen Cook, Cameron Steel, Graham Clark, Paul Coughlin, Ryan Pringle, Stuart Poynter (wk), James Weighell, Chris Rushworth, Barry McCarthy, George Harding, Gavin Main.
Michael Hogan will begin his reign as Glamorgan captain when they host Durham in County Championship Division Two at St Helen's on Friday.