The 38-year-old has coached in Germany and Scotland, most recently as Felix Magath's assistant at Hertha Berlin.
His deal runs until 2025 and he will take charge at Reading on Saturday.
Schofield's nine league games yielded seven defeats, prompting the Terriers to terminate his contract with the club 23rd in the Championship table.
"We have explored a wide range of options in our search for our next head coach, and Mark became our first choice after our very first meeting," Town head of football Leigh Bromby said.
"His beliefs in coaching and football fit very well with our methods at the club, and we also believe he can also add to what we do because of who he has worked for and with during his career so far."
Fotheringham, a former Celtic trainee who played for clubs such as Dundee, Freiburg and Norwich during a 276-game career, has served his coaching apprenticeship in spells at Fulham, Ingolstadt and Karlsruhe - with this his first managerial job.