The addresses will culminate in a speech by May outlining the government's ambitions for a future partnership with the European Union after the country's departure from the bloc in March, 2019.
"Brexit is a defining moment in the history of our nation," a Downing Street source said.
"We will be forging an ambitious new partnership with Europe and charting our own way in the world to become a truly global, free trading nation.
The series will begin next week when Foreign Secretary Boris Johnson makes "a rallying cry to those on both sides of the Brexit debate," according to Downing Street.
Also Read
May will then detail hoped-for new security arrangements with the EU at the Munich Security Conference yesterday.
A further three speeches are planned for the next two weeks before she makes a second address.
Brexit Secretary David Davis will discuss business standards, Cabinet Officer minister David Lidington will talk about devolution, while Trade Secretary Liam Fox will detail future global trade deal strategy, No. 10 said.
There they will bid to thrash out substantial differences over the future relationship with Brussels.
Finance minister Philip Hammond, seen as a Brexit sceptic, is not slated to deliver one of the touted speeches.
Justice Secretary David Gauke denied today there was a "plot to gag a particular faction of ministers."
"I don't think that's a fair characterisation at all," he told ITV.
Meanwhile, after Japanese business leaders who met May in Downing Street this week expressed concern about the Brexit's potential impact, International Development Secretary Penny Mordaunt said the coming weeks would give them "some answers".
Despite a warning on Friday from EU negotiator Michel Barnier that a post-Brexit transition period was being endangered by substantial ongoing disagreements, Mordaunt predicted "common sense will prevail".
"The other nations involved in this are very pragmatic and have not been impressed with some of the language that the Commission has used," she added.
Disclaimer: No Business Standard Journalist was involved in creation of this content