The platform says it will never sell user data and relies on "the generosity of individual donors" rather than ads.
Those who do sign up are added to a waiting list and asked to invite others, or choose a subscription payment.
It is positioning itself as a "news focused" place, and says members will be able to edit "misleading" headlines.
They will see the articles shared by their network in a timeline format, appearing with the newest first rather than algorithmically to try to appeal to their interests.
The subscription is £10 per month or £80 per year in the UK (€12 / €90 in Europe, $13 / $100 in the US).
"We will empower you to make your own choices about what content you are served, and to directly edit misleading headlines, or flag problem posts," reads the introduction to WT:Social.
"We will foster an environment where bad actors are removed because it is right, not because it suddenly affects our bottom-line."
In a recent interview with the Financial Times, Mr Wales described the advertising-led business model favoured by the social network giants as "problematic".
"It turns out the huge winner is low-quality content," he said.
Mr Wales launched a crowd-sourced news platform called Wikitribune in 2017, aimed at tackling fake news.
However, in October 2018 it let go of its team of professional journalists.
WT:Social is a separate entity to Wikipedia.
Social media consultant Zoe Cairns said she thought the network would have to grow its numbers quickly in order to prove itself to be a viable alternative to the giants.
"It's going to need a lot of money ploughed into it," she said.
"People are so used to social media being free. I think businesses might pay for it, but people are so used to having news at their fingertips for free."
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