The venue is hoping to replicate the success of its famous 1970s company, which included future stars like Julie Walters, Bill Nighy and Jonathan Pryce.
It did away with its resident company in 1992, instead casting different actors for each play.
The new company will include Richard Bremmer, who played Voldemort in the first Harry Potter film.
He will be joined by Melanie La Barrie, who played Mrs Phelps in West End hit Matilda, and Patrick Brennan, who was headmaster Mr Dawes in Downton Abbey.
As well as the more experienced hands, the new company includes 23-year-old Emily Hughes, who graduated from drama school this year and was recruited through an open audition, and Elliott Davis, who has risen through the venue's youth theatre.
The seven men and seven women will perform in five shows, ranging from Romeo and Juliet to children's theatre to a new Toxteth-set drama, between February and July 2017.
Everyman artistic director Gemma Bodinetz said: "Anybody that inherits this job comes with this massive shadow hanging over them of the glorious, wonderful mid-'70s, when there was a very famous company here.
"So you're always aware that there was this magical time when actors like Julie Walters, Pete Postlethwaite, Jonathan Pryce, Matthew Kelly - all these phenomenal actors came out of a rep company.
"And you ask yourself, was that just the time, was that just a phenomenal flowering that could never happen again?"
She wants audiences to get to know the actors and for the company to have a "conversation" with the city, she explained.
"We live in a very potent city and these are very exciting, tricky times, and it felt like it was time for this theatre to have a unique voice again."
Resident rep ensembles were the norm in regional theatres during much of the 20th Century. But of those that survived into the 1990s, most died off in the recession at the start of that decade.
A few venues - such as the Royal Shakespeare Company and Dundee Rep - still use the system, while the Donmar Warehouse in London recruited an all-female company for its current Shakespeare trilogy.
In Liverpool the actors will perform in one play at night while rehearsing for the next show during the day.
La Barrie said she was not used to having more than one part in her head at any one time. "Working in a rep company is not something that most modern actors are used to," she said. "It's going to be interesting to see what we remember."
But being part of a company was "every actor's dream" because they must "utilise every single bit of your skill", she said.
Hughes said she was "inspired" by the Everyman's past and the history of the rep system.
"Coming out of drama school, it was something that people talked about that used to happen years ago," she said. "'What a wonderful system - but it doesn't really happen any more'."
"So when the news [of the new Everyman company] broke I was straight in there, like, 'Oh my God, I have to do this'."
Bodinetz said she had big ambitions for the company in the future. "In my dreams, the Everyman Company becomes an exciting brand and we tour the world with it once we've performed here," she said.
The full Everyman company: Richard Bremmer, Patrick Brennan, George Caple, Pauline Daniels, Elliott Davis, Laura dos Santos, Emily Hughes, Tom Kanji, Melanie La Barrie, Asha Kingsley, Dean Nolan, Zelina Rebeiro, Keddy Sutton, Liam Tobin.
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Liverpool's Everyman theatre has named the 14 actors who will form its first repertory company for 25 years.