The Blues tonight announced a deal had been done with the Premier League club for the 17-year-old Cumbrian.
United have not said how much they have sold the teenager for.
They described the fee as "substantial" and said it included clauses that could benefit the club in future.
The Cumbrians said Wigton-based Branthwaite, whose agent is the ex-Carlisle striker David Reeves, had turned down the offer of a new three-year deal at Brunton Park two months ago.
In a statement director of football David Holdsworth said: “Ideally this fantastic young man would still be our player, but I think everyone will appreciate and understand that it can become very difficult for the individual when clubs at the highest level – some of the biggest clubs in the country – come calling and showing an interest in your services.
“We did what we could, but we have to respect the wishes of the player, his family and those who advise him.
"Once it becomes apparent that a player does want to move, all you can then do is work hard to get the best possible deal for the club.
“It is an excellent deal for Carlisle United in terms of the financial aspects, both now and in the future, and Everton are getting a young man who we think will make a big impact.
“I’m sure we all wish Jarrad the very best as he makes this move to Everton and the Premier League.”
The move follows a period when Branthwaite has been out of the team, Carlisle claiming he had missed their last game on Saturday through "illness".
Everton, though, unveiled Branthwaite tonight and said he has signed a two-and-a-half year deal, and will go into their under-23 squad.
He was quoted on the Everton website as saying: “The pathway is superb – that’s what made me want to join Everton.
“I’ve seen those players get their chance in the first team and do well.
“I just can’t wait to get started. Everton is a big club and I’m buzzing to be here."
Branthwaite is the third home-grown player to be sold recently by the Cumbrians, after the moves of Liam McCarron and Josh Galloway to Leeds.
Blues head coach Chris Beech said in a press conference today there had been "two bids" from "top-class" clubs for Branthwaite over the weekend, but that he did not know who those clubs were.
Beech also said England's Under-18 and Under-19 coaches had been monitoring the defender, who had been eyed by other top-flight clubs including Watford.