Mr Crompton was suspended by Dr Alan Billings, the region's Police and Crime Commissioner (PCC), following a statement he made after the end of the Hillsborough inquest verdicts in April last year.
In September, Mr Billings called for Mr Crompton's immediate resignation.
Mr Crompton, who had already said he would retire in November, tendered his resignation the same day.
Her Majesty's Inspectorate of Constabulary described the move as the "forced removal" of the Chief Constable.
Mr Crompton's lawyers claim that Dr Billings's decision to call upon him to resign or retire was unreasonable, irrational or disproportionate and, today, they will ask Lady Justice Sharp and Mr Justice Garnham to declare it unlawful.
The judicial review comes after Dr Billings said that Mr Crompton had led a force that put "its own reputation first before considering victims" of the Hillsborough Stadium disaster.
Mr Crompton has described the PCC's resignation call as "fundamentally wrong".
He was suspended after an inquest jury concluded police conduct contributed to or caused the deaths of 96 football fans in 1989.
The families of those who died complained to the coroner and claimed a line of questioning by South Yorkshire Police was designed to try and blame the fans for the disaster.
After the inquests, Mr Crompton appeared to justify the questioning of the fans' conduct.
Summarising his reasons for asking the chief constable to immediately resign, Dr Billings said the statement showed Mr Crompton did not "grasp the gravity of the situation".
He added the statement was "insensitive and damaged both the force and the Chief Constable himself".
The hearing in London is expected to last two days.