Dorahy, back in Great Britain after being sacked by Wigan at the end of the 1993-94 season, is the replacement for his fellow-Australian, Brian Johnson, who resigned as coach after Wire's record 80-0 defeat by St Helens earlier this month.
Murphy, who shares the distinction of being sacked by Wigan - in his case in 1984 - takes the new role of rugby football executive, promising yesterday, with his tongue only slightly in his cheek, to keep out of selection matters.
"John Dorahy will come back to haunt Wigan," he predicted, showing that 20 months out of the game since being made redundant by Huddersfield have not robbed him of his dexterity with a soundbite.
Dorahy, plagued by personality clashes with senior players at Wigan, took the opportunity to hit out at the account recently published by one of those players, the now Leeds coach, Dean Bell, labelling it "fiction".
The former Halifax coach, whose distinguished playing career included spells at Western Suburbs, Manly and Hull KR, was eventually sacked, after winning the championship and Challenge Cup, following a confrontation with the Wigan chairman, Jack Robinson.
"The difference at Warrington is that I will have 100 per cent backing," he said of that stormy episode.
"John Dorahy will bring a new style of winning, entertaining rugby to Warrington," promised Murphy, who coached Warrington with great success from 1971-78 and whose own departure from Central Park came when he threw a phone at the then chairman, Maurice Lindsay.
Entertainment off the field is almost guaranteed from the new Warrington regime, which was completed yesterday by the appointment of another former Wigan employee, John Fillingham, as commercial manager, with a brief to raise finance for the acquisition of what Murphy termed "only the very, very best players".
Dorahy and Murphy will have their first look at what is currently at their disposal in the Silk Cut Challenge Cup fourth-round tie at Oldham on Sunday, although the assistant coach, Clive Griffiths, overlooked for the job he has been doing as a caretaker, will have the main voice in team selection for that game.
John Myler has resigned as Academy coach at St Helens, in protest against the sacking of Eric Hughes.
"It is not a rush decision, but I felt I had to make stand," Myler said. Saints' new coach, Shaun McRae, is expected to arrive at the club tomorrow.
Bradford Bulls have completed the signing of the Australian scrum-half, Glen Tomlinson, from Batley, in exchange for Roger Simpson, David Turpin and Phil Hardwick, plus a small cash adjustment.
Tomlinson, who was also a target for Leeds, is going to Australia for a family wedding and will return in time to start training for the start of Super League in March.