Users will be able to buy verified status on the micro-blogging site.
In an update for Apple devices, the company said the feature would be open to users in certain countries.
There is concern that the platform could be swamped with fake accounts.
Around half of the company's workforce was laid off on Friday.
The blue tick was only available to people who were asked to prove their identity.
It has been used as a sign that a profile is authentic, and is a key tool to help users find reliable information on the platform.
Government figures, celebrities, journalists and brands could be impersonated by anyone willing to pay a monthly fee if the policy change is anything to go by.
Following his acquisition of the firm late last month, Mr Musk appears to be looking to make more money from other sources.
The cuts, as well as Mr Musk's advocacy of free speech, have caused speculation thatTwitter could water down its efforts on moderation.
Mr Musk said that the firm's stance towards harmful material remained the same.
The Human Rights Commissioner of the United Nations urged Mr Musk to ensure that human rights are central to the management of the social networking site.
This was not an encouraging start under Mr Musk's ownership, according to the UN intervention.
There was no reply from the social networking site.
Following Saturday's announcement of the change in verification policy, the price of the blue subscription in the UK remained at its previous price of just under five dollars a month.
The changes would only be applied in the UK, US, Canada, Australia and New Zealand, according to the update.
The changes would be rolled out around the world after they were observed in a few countries, according to Mr Musk.
It wasn't clear what would happen to the profiles which already had a blue tick, or if they would still be able to use the service.
Mr Musk said the timelines for changes to be implemented were a couple of months.
He answered a question about the risk of users pretending to be notable figures and said that the account would be suspended.
Mr Musk said that users would soon be able to attach long-form text to their messages.
Jack Dorsey apologized to employees for what had happened at his former company.
The former CEO of the company said he was aware that staff were angry with him.
I'm responsible for why everyone is in this situation, because I grew the company too quickly. I apologize for that
The need for dismissals seemed to be endorsed by Mr. Dorsey. He supported Mr Musk's takeover in the past.
A number of major brands have stopped advertising with the social networking site.
Mr Musk wants to decrease the platform's reliance on adverts, and Saturday's update promised half the ads.
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