Despite a backdrop of upto £2 billion of cuts expected in next year's Scottish budget, Mr Gray will tell delegates that the 20,000 lowest paid workers in the public sector in Scotland will earn no less than £7 an hour.
A Labour administration will also pressurise private sector contractors working for the Scottish public sector to follow suit or risk being excluded from the preferred contractor list.
The idea, first tried out two years ago by Glasgow City council under Stephen Purcell's leadership, is meant to be a signal that a new Labour Scottish Government would prioritise helping the less well off. The initiative would be partly funded by freezing the pay of public sector staff who earn more than £100,000.
Mr Gray will tell conference: "There are going to be difficult decisions and there will have to be pay restraint in the public sector, especially at the top.
"But Labour values demand we protect the lowest paid. That is why we are committed to a Scottish living wage of over £7 set by a Scottish living wage unit.
"Labour will introduce it in the public sector, but the Scottish living wage unit will campaign for it to be rolled out across Scotland to all sectors of the economy. One way would be through public sector procurement contracts."
Mr Gray's will be followed by shadow Secretary of State for Scotland, Jim Murphy MP, who will attack the cancellation of the Future Jobs Fund as "policy immorality of the coalition laid bare - a gang of cabinet millionaires taking away jobs from unemployed kids."
He will say: "It look Thatcher six years to cut support for the unemployed.
"This government did it in six weeks. The Lib Dems are part of a Tory government that's going where Thatcher feared to tread. Nick Clegg has sold his soul."
But the idea of a new higher minimum wage has been described as "old" by the SNP. An SNP spokesman said: "The SNP has led the way by freezing ministerial pay and restraining pay at the top of the public sector."