Allison Hunter, a former teacher, has been selected by her group at Glasgow City Council to succeed James Dornan, who became MSP for Cathcart last month.
One party source said Ms Hunter has respect across the political spectrum. Another said that after a volatile year for Glasgow's SNP group she will keep a lid on any tensions, adding that she now intended to stay on until after 2012.
Ms Hunter is also known to have the backing of many in the party's hierarchy and was Nicola Sturgeon's election agent in 2007, a role her daughter carried out during last month's election.
Councillor Hunter has maybe the most formidable job of any Glasgow SNP councillor for a generation, with belief high the party can take the council from Labour next year.
She said: "Today is the first day of our campaign to win Glasgow City Council. This group is united in our ambition to become the largest party in the council and wrest control of the city from the tired hand of Labour.
"I am delighted to be following two successful leaders, both now MSPs, John Mason and James Dornan, who have done much to prepare us for the next 12 months.
"We have a strong base to work from, following our hugely successful and positive Holyrood election campaign.
"We have a talented team and a strong pool of local candidates – combined with our positive message for the people of Glasgow – we are ready for the campaign to come."
One party source said: "Allison's no mug and this was the sensible choice by the SNP group. She's more than capable of taking the group into next year's election and will show you don't need to shout to perform well as a leader."
Former SNP group leader James Dornan MSP said: "Allison will be an excellent leader for the SNP as we enter a crucial election for council."
Labour is urged to axe MSP over colleague abuse
Labour has come under pressure to axe a newly-elected Labour MSP forced to attend an anti-racism course after verbally abusing and intimidating an ethnic-minority colleague.
Anne McTaggart, who is also a Glasgow councillor, was recently handed a key role on local authority personnel matters and has adjudicated in several hearings in recent months.
Last night the SNP said Labour must suspend the Glasgow MSP as other councillors in the city have been in the past year.
It was revealed at the weekend that when she was employed by the city council's social work department, Mrs McTaggart was suspended from her duties after a series of complaints against her were upheld.
She was also moved to another job and attended an anti-racism course in 2006.
Despite this, in February she adjudicated in the unsuccessful redundancy appeal by a man with cerebral palsy who designed children's play-parks.