Ms Murphy, 51, disappeared on February 4.
Stephenson was arrested early Wednesday morning and charged Thursday afternoon.
The police will provide an update on the case on Thursday at 3:45 p.m.
Stephenson is the only son of legendary AFL Tigers player Orren Stephenson, whose AFL career included playing for Geelong just over a decade ago.
Police confirmed the alleged killer would appear in the Ballarat Magistrates’ Court on Thursday afternoon charged with murder.