Mr Murphy is the third politician to announce their intention to run for the post vacated by former leader Johann Lamont on Friday.
Speaking in a national newspaper, Mr Murphy, a former Scottish Secretary, said he wants to the party north of the border make a "fresh start" in the wake of the referendum.
He said: "I think it is time for a fresh start for the Scottish Labour Party. I am proud of the Labour Party and I am proud of Scotland but I am not satisfied.
"I want to strike a tone that stops the Scottish Labour Party committing self harm.
"I want to unite the Labour Party but, more importantly, I want to bring the country back together after the referendum."
Mr Murphy joins Lothians MSPs Neil Findlay and Sarak Boyack as contenders for the Labour hotseat in Scotland.
Nominations for the post open on Friday with voting due to open on November 17 before the winner is formally announced on December 13.
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