The gatherings will be run along the lines of a traditional church service, but the strains of All Things Bright And Beautiful might be swapped for a sing-a-long to Eye Of The Tiger and preaching replaced with a talk on positive thinking.
The first "Sunday Assembly" - as these atheist church services are known - was held in London at the beginning of this year, stemming from an idea by stand-up comedians Sanderson Jones and Pippa Evans.
This month and next, they plan to launch another 30 satellite 'congregations' in cities from Leeds to Chicago and Vancouver to Adelaide.
As part of it, the Sunday Assembly will begin to be held on a regular basis for the first time in Scotland, with monthly events in both Glasgow and Edinburgh, where one-off services have previously taken place.
But the idea is divisive within the world of atheism with some calling it barmy and an "aping" of religion.
Robert Concannon, who is helping to organise the Sunday Assembly in Edinburgh, said: "There are lots of communities which are available for people to do the whole angry atheist thing. This is specifically not about that, this is an opportunity to get all the good bits of going to church but without the need for invoking anything supernatural."
He added: "A lot of us are ex-religious who feel the lack of community when you drop the religion."
While details of the service are still being worked out, Concannon said it would involve a speaker, a poetry reading and a moment of silence. In Edinburgh, the service will take place in a city-centre bingo hall.
"It will follow a fairly traditional church service-type format, only with better songs," he said.
"I adore hymns and I still have a hymn book on my piano - but the words are dodgy and I don't like them." On the songs that will be sang at the Sunday Assembly, he added: "It is popular songs that everyone can sing along to - it is really nice to get that singing in a group feeling."
The Sunday Assembly founders claim it is catering to the fastest-growing belief group - those who do not count themselves as religious.
Figures from the 2011 census, published earlier this month, revealed the number of people in Scotland who regard themselves as non-religious stood at 37% - with numbers rising from 1.4 million to 1.9 million over the past decade.
It meant those in the "non-religious" category overtook the biggest denomination, the Church of Scotland, for the first time.
According to the census figures, just over half of the country - 54% - still think of themselves as Christian.
Gary McLelland, one of the organisers of the Sunday Assembly in Glasgow, who is also chair of the Edinburgh Secular Society, is keen to hold more regular services if the idea takes off.
"The hope is the more people get involved and spend their time with it, then we might move to perhaps fortnightly or weekly services", he said.
McLelland said the Glasgow launch will include a talk by psychologist Patricia Elliot and "positive secular uplifting songs", citing the example of Eye Of The Tiger by Survivor, which was played at a Sunday Assembly he attended in Edinburgh. But he is keen to develop the idea beyond just a get-together. He hopes the congregation would develop into taking part in community outreach work, for example running soup kitchens.
He said: "It is generally one of the most positive aspects of organised religion. So I think there is a growing consensus among people who aren't particularly religious that they want to get involved in doing something like that themselves."
The Sunday Assembly doesn't entirely steer clear of allusions to religion, sometimes using tongue-in-cheek biblical references. The launch of the satellite congregations is being dubbed "40 days and 40 nights: The Roadshow".
Both the Church of Scotland and the Catholic Church in Scotland declined to comment.
But Nick Spencer, research director of Christian think tank Theos, says the idea is not new. "They sprang up a hundred years ago, with people who had lost their Christian faith," he said.
However, Spencer, who will publish a book on the history of atheism next year, said the so-called ethical churches formed in the late 19th century had fizzled out by the 1930s, from a failure to find a common cause.
"I suspect it is quite an urban phenomenon and it is people who lack a sense of community and meaningful relationships in an otherwise anonymous and individualised culture."
Not all of those who challenge the role of religion in society back the concept of an atheist church.
Terry Sanderson, president of the National Secular Society, branded it a "barmy" idea.
"If you want to have religion, go and get the real thing instead of this pretend one," he said.
Sanderson acknowledged that it did seem to have "caught people's imagination".
He said: "The bigger it gets, the more likely it is that people will disagree, fall out and split off. "
The Sunday Assembly will be launched in Edinburgh on Tuesday, October 22 and Glasgow on Wednesday, October 23. Visit www.sundayassembly.com