Her decision to quit comes a month after she helped lead the successful No campaign in the independence referendum.
It is believed Ms Lamont was fed up with internal sniping about her leadership and was critical of party bosses in London for not allowing the Scottish party more autonomy.
Last night Ms Lamont was reported as saying: “I am standing down so that the debate our country demands can take place.”
But a source close to the Glasgow Pollok MSP said her resignation letter, which will be made public today, would contain “a kick at Ed Miliband and the Scottish Labour MPs at Westminster”.
The outgoing leader is also reported as saying: “I am proud of what we have achieved over the last three years. We held Alex Salmond to account. I firmly believe that Scotland’s place is in the UK and I do not believe in powers for power’s sake.
“But colleagues need to realise that the focus of Scottish politics is now Holyrood, not Westminster.”
Last night a source said Ms Lamont “has a hard message” for Labour’s Westminster leadership who have thwarted her attempts to lead the Scottish party.
He said: “All some people think is necessary is to change the face of the party. That’s not the case.”
Sources close to Ms Lamont say she had been deeply unhappy about the way the UK party handled the investigation into alleged wrongdoing in the Falkirk constituency Labour party.
She was also frustrated at the way the UK leadership acted during the party commission that formulated its blueprint for further devolution to Holyrood.
“There was a feeling the party had to be more autonomous, and some of that was shown up during the devolution commission,” said a source close to the MSP.
“But she bit her tongue and got on with it during the referendum. Now there is no point in going on.”
It is understood the final straw for Ms Lamont came with the UK party’s treatment of Scottish Labour general secretary Ian Price.
Mr Price is to leave his job after only 18 months as the Scottish party’s most senior full-time official amid reports he was marginalised during the independence referendum campaign.
Mr Price had been called down to London and was “in the process of being dismissed”, according to sources, a move Ms Lamont felt undermined her.
The source said: “The treatment of Ian Price was the straw that broke the camel’s back. Johann felt she was not fully consulted.”
Scottish Labour deputy leader Anas Sarwar MP will take over temporarily while it is likely senior MSP Jackie Baillie will represent Labour at First Minister’s Questions in the interim.
Ms Lamont has faced increasing speculation over her position since last month’s referendum, in which four traditional Labour areas, including Glasgow, voted Yes.
Earlier this week, two former Labour first ministers, Lord McConnell and Henry McLeish, suggested the party was in need of an overhaul. Lord McConnell, first minister between 2001 until 2007, said the party must “rediscover our sense of purpose, our vision for Scotland”.
This view was shared by his predecessor Mr McLeish, who said: “There’s no entitlement to a vote now. Labour has got to realise that every vote has got to be fought for.”
Ms Lamont, 57, was elected as the party’s leader in December 2011, having previously acted as its deputy leader.
She served as a junior minister in the Labour-Liberal Democrat coalition Scottish Executive from 2004 until the coalition’s defeat at the hands of the SNP in 2007.
She was born in Glasgow to Gaelic speaking parents from the Hebridean island of Tiree.
She grew up in the city and obtained a degree in English and history from the University of Glasgow before becoming a teacher.
Joining the Labour Party in 1975, she was active in the university’s Labour Club. She was also involved with the women’s movement and became a representative on the Scottish Constitutional Convention, the body that paved the way for Scottish devolution.
She has previously told how she voted No in the 1979 referendum, later saying: “I came from the strand on the left which saw the politics of nationalism as a diversion from more central aims but later came to see the parliament as a vehicle for democratic change in Scotland.”
She was a member of the Scottish executive committee of the Labour Party, serving as chair in 1993.
Ms Lamont was chosen as a candidate to represent Labour in 1998 and was first elected as the MSP for Glasgow Pollok in 1999.
She held the seat in 2003, when she faced a strong challenge from Scottish Socialist Party leader Tommy Sheridan, and then again in 2007 and 2011.
Ms Lamont, a mother-of-two, stood for the party leadership in Scotland following the resignation of Iain Gray in the wake of the 2011 Scottish general election defeat.