The commission’s report, setting out a series of specific proposals on issues from housing to pay, will be discussed by councillors next week.
Council leader Adam McVey said tackling poverty was already one of the authority’s key priorities.
He said: “We know that the pandemic has been incredibly challenging for those who were experiencing or at risk of poverty in our city. The commission has pulled no punches and got to the heart of the issues - while there is no doubt that the pandemic has exacerbated the situation, poverty in Edinburgh is a crisis that goes beyond one cause and we cannot ignore it.
"If we’re to make progress on the scale required, it needs a concentrated effort from us, our partners and allied organisations, local business and residents acting as one Team Edinburgh.”
Over 77,000 people are living in poverty in Edinburgh, including one in five children.
The commission said funding to ensure 20,000 new social homes over the next decade was the top priority, but also called for the Capital to become a Living Wage City next year, urged action to close the education attainment gap and proposed a new Edinburgh Guarantee on job or training opportunities for people of all ages.
Lothians Labour MSP Sarah Boyack said the commission’s findings were sadly not surprising.
"High rental costs and low pay are pushing more families into hardship, and for one in five children to be living in poverty in this wealthy city is absolutely unacceptable.
“Edinburgh is a wonderful city with many opportunities but there simply isn’t enough social housing, and with the impact of the pandemic, job security is worse than ever.
“I have pushed repeatedly for an increase in social housing stock. I have raised the issue of the SNP Government’s proposed real terms cut in affordable housing in this year’s capital budget with the Finance Minister and also in our evidence session to the Local Government Committee today.
“We must have a more holistic approach if we are to properly challenge homelessness and poverty: job security and investment in low carbon infrastructure, a living wage, greater private rental market regulation and better access to health and wellbeing services.
“The pandemic has laid bare the extent and depth of social inequalities across the country. However, we need to make Edinburgh a welcoming and affordable place for families to live and work.
Nicola Hazelton, Shelter Scotland Edinburgh Community Hub manager, said the
“This report spells out the truth: high housing costs are pushing people into poverty in Scotland’s capital. There’s no way of ending this situation without fixing the housing emergency.
“It can’t be right that despite living in Scotland’s wealthiest city, as many as 20 per cent of children are growing up in poverty, which we know will damage their health, wellbeing and future life chances.
“The commission’s report sets out the scale of the ambition required to build the social homes that Scotland needs to transform the lives of people in this country, creating stability, improved health and wellbeing and opening the door to opportunities.”