Slack was rumoured to have been offered the job a couple of weeks ago, following news of the departure of Helen Bower and Greg Swift, respectively May’s spokesperson and deputy spokesperson.
Downing Street has now confirmed the appointment in a short statement on its website.
Last year, the Civil Service Jobs website advertised for a new spokesperson for the PM on a salary of £87,000, with a closing date of 13 January. Interviews were due to conclude late last month.
One Westminster source told PRWeek: "I think they've done it on a very hefty package.
"He's come in at Theresa's request. [Daily Mail editor] Dacre really likes James, thinks he's shit hot, Theresa really likes James. You see they've got a common interest; they're not going to kick up much of a fuss about it. It shows the alignment between The Mail and Downing Street right now.
"James will be a much more high-profile role than a normal PMS. Technically he'll be a civil servant but he's going to have parity, pretty much, with Katie [Perrior, Downing Street director of communications]."
The source said Bower and Swift "got completely frozen out" in their roles. "It was quite brutal. Helen was the Prime Minister's official spokesman, but she wasn't even getting in to see the PM much. There's been a complete clear out."
Separately, Will Walden, Public Affairs MD at Edelman and Boris Johnson’s former communications director, told PRWeek: "Slack’s appointment is a super-smart move by Number 10. He’s a good operator, he’s trusted by the lobby, and he’s no-nonsense. Inevitably his ex-colleagues will now expect more of an insight than they’ve been getting.
"If they’re wise, Number 10 will give him what he needs - unfettered access to the decision-making and greater autonomy in his dealings with the press."
Bower, who has worked in various roles in Downing Street since 2011, is to join the Foreign Office as director of communications.
Former Daily Express journalist Swift, who joined the Downing Street comms team under David Cameron in April 2016, is moving to the Department for Exiting the European Union following Slack’s appointment.