The campaign is expected to be a head-to-head between MSPs Kezia Dugdale and Ken Macintosh.
Mr Macintosh has launched his campaign with a promise to shake up the party organisation, including moving the headquarters from Glasgow to Edinburgh.
He said Scotland must be more accountable and responsive to the needs and wants of Scottish people.
Ms Dugdale will launch her leadership campaign on Saturday. She has said she will offer the party a fresh face and fresh thinking.
Mr Macintosh said that if he became leader he would begin negotiations with the new national Labour leadership to establish a formal relationship with Scottish Labour that recognises its autonomous role within the UK party.
He said that was one of several fundamental changes to the way Scottish Labour operates that were needed before the party could win back voters' trust.
The MSP for Eastwood's reforms would include:
Launching his leadership campaign at the headquarters of East Kilbride and District Engineering Group Training Association, Mr Macintosh said: "I want to make it quite clear - I see myself as the change candidate.  Yes we could manage the situation we are in.  We could lurch from election to election as we have done in the past.
"But I want to change the whole way the Labour Party operates. I want to move away from the machine politics of the past, to give the party back to its members and to the people we want to represent."
He added that his leadership would seek to assert the "identity, authority and autonomy of the Scottish Labour Party".
"I've never been interested in standing for Westminster and I don't look over my shoulder or seek permission to say what I want to say on behalf of the people of Scotland.
"The Welsh Labour party seems to have had no difficulty in establishing its own identity, with significantly less devolved power or responsibility than we enjoy here in Scotland."
He said: "We will be entirely in charge of our own affairs and our own decision-making, but it is important to us that we have a partnership of equals with party colleagues in the rest of the UK.  As I heard it described recently, our future will be one of both self-rule and shared-rule."
On his plan to move the party's head office to Edinburgh, he added: "It is time the structure of the Labour Party reflected that the focus of political attention in Scotland is Holyrood.
"This will be the head office - we will opt in to the Labour Party, we will choose to be members of something bigger, but control rests with members here in Scotland."
He said he was committed to devolution and wanted to devolve responsibility within the party to eight regions reflecting the list regions of the Scottish Parliament, with membership and campaigning organised at that level.
Speaking about his plan to put all elected representatives on an equal footing within the party, he said: "I want to broaden our appeal, not narrowly focus on an ever declining audience of Scots with so-called traditional Labour values; not solely concentrate on former industrial heartlands in the central belt, but reach out to every place and part of Scotland."
Three candidates are expected to campaign for the deputy leadership role: Glasgow City Council leader Gordon Matheson and MSPs Alex Rowley and Richard Baker.
The hustings period begins on 22 June and the result will be announced on 15 August.
The elections were sparked after leader Mr Murphy and his deputy Ms Dugdale resigned from their positions.
The changes at the top of the Scottish party come in the wake of Labour losing all but one of its 41 seats in Scotland in May's general election.
Following changes pushed through by Mr Murphy before his departure as leader, the election for both the leader and deputy leader will be based on one-member-one-vote.
All the contestants will take part in a series of hustings at four venues:
The results of the two contests will be announced at a special gathering on Saturday 15 August.
15 June - Nominations open for leader and deputy leader
19 June (12 noon) - Nominations close
19 June (17:00) - Supporting nominations open
22 June - Hustings period opens
13 July - Last date to join as member, affiliated supporter, or registered supporter in order to vote in the leadership ballot
10 July (12 noon) - Supporting nominations close
20 July - Ballot opens
14 August - Ballot closes
15 August - Result announced
Nominations have closed in the contest to replace Jim Murphy as Scottish Labour leader.