"Our City" is being distributed from Monday with details of councillors, information and stories.
A quarterly version was axed in Bristol in 2011 to save money. Council-run newsletters have been criticised as "Town Hall Pravdas" in the past.
But Mr Ferguson said the magazine was "very economically produced".
"A lot of people complain to us they don't get enough information, they don't access the internet," he told BBC Radio Bristol.
"This is a very economical, sustainable way of getting to each household."
He told the BBC it would replace information lost when the Council Tax Booklet was reduced from 40 pages to eight, in 2014. It includes an updated list of councillors, as well as news stories and information about local services.
The latest publication is a trial and it has not yet been decided if it will be repeated. Of the £34,000 total cost, £9,000 will be paid for by advertising by Bristol 2015, the company set up by the council to run its Green Capital events.
Last year the then Communities Secretary Eric Pickles said "municipal state-produced newspapers" wasted public money and undermined free speech.
But Mr Ferguson, who will stand for re-election next year, said the magazine was the first one produced during his time in office, and added:  "I did not decide one word that goes in, except for my foreword."
He told BBC Radio Bristol he was "embarrassed" there were four photographs of him in it and said: "I certainly wouldn't have chosen that."
Bristol Mayor George Ferguson has defended a free magazine being sent out to homes at a cost of £34,000 - saying not everyone uses the internet.