The First Minister is using the cash Scotland gets from the UK Government to pay for the meals, following Nick Clegg's announcement last year to fund a similar policy in England.
Mr Salmond said it would remove the possibility of free school meals being seen as a stigma and would save parents more than £300 a year.
There are almost 16,000 pupils in P1-3 classes across Glasgow and extending the entitlement to all means an extra 6000 will be eligible.
The move was welcomed by anti-poverty campaigners, who have been calling for free meals for several years.
Gordon Matheson, leader of Glasgow City Council, said Glasgow should receive £7million from the £60m allocated to Scotland from Westminster
He said: "Glasgow has consistently shown its commitment to young people by providing free breakfasts and free lunches for thousands of children in our schools.
"I repeat today what I said when Nick Clegg first announced this policy, namely that Glasgow must receive our £7m fair share of this extra money.
"The Scottish Government has recently short-changed Glasgow's budget of £153m of funding for services in the city. It's vital we're not ripped off again."
John Dickie, head of the Child Poverty Action Group (CPAG) in Scotland, said: "Current means-testing means too many of our worst off children are not receiving a free school meal and parents too often struggle to meet the extra costs of lunches as they move back into work or increase their hours when their children start school.
"What's more, a universal approach ensures that all our children, whatever their home circumstances, gain the health and education benefits of a healthy lunch in the middle of the school day."
Labour leader Johann Lamont said the poorest children already get free school meals.
She said: "By extending it to everyone else he (Mr Salmond) has chosen to spend the money on everyone but the poorest children."