The moves had been widely expected and were announced by both teams on Tuesday.
Leclerc, a Ferrari protege who has been long tipped for promotion to the sport's oldest and most successful team, made his debut with Sauber this season after winning last year's Formula Two title.
He will now partner four times world champion and title contender Sebastian Vettel.
"Scuderia Ferrari announces that, at the end of the 2018 season, Kimi Raikkonen will step down from his current role," said Ferrari.
"As a world champion for Scuderia Ferrari, he will always be part of the team's history and family. We thank Kimi for all of this and wish him and his family a prosperous future."
Ferrari are Formula One's most glamorous team and Leclerc will be one of the youngest and least experienced drivers to race for them.
Raikkonen, 38, posted a message on Instagram announcing he would be rejoining Sauber - a team with Ferrari engines and Alfa Romeo sponsorship - on a two-year deal.
The Finn first drove for them in 2001, before moving to McLaren and then on to Ferrari, where he won a title that remains the team's most recent.
"Guess who's back?! Next two years with @sauberf1team ahead! Feels extremely good to go back where it all began!" he told his 974,000 followers.
IMPORTANT PILLAR
Sauber said the move, which keeps three world champions on the starting grid next season after Spaniard Fernando Alonso's departure from the sport, represented "an important pillar of our project".
"Kimi's undoubted talent and immense experience in Formula One will not only contribute to the development of our car, but will also accelerate the growth and development of our team as a whole," said principal Frederic Vasseur.
Sauber are ninth out of 10 teams ahead of Sunday's Singapore Grand Prix, an improvement on last year when they were regulars at the back.
Raikkonen, known as the 'Iceman', turns 39 next month and is the oldest driver on the grid as well as one of the most popular.
More than 87,000 fans had signed an online petition, meaningless in the circumstances, in the last week urging Ferrari to retain him.
Vettel would also have been happy to continue the partnership with a team mate he has got on well with, and beaten on a regular basis, but the decision was not his to make.
The late Ferrari chairman Sergio Marchionne had flagged up Leclerc as Raikkonen's obvious successor last year already.
The youngster will be the first native of the Mediterranean principality, which hosts the sport's most glamorous race, to drive for Ferrari.
Managed by Nicolas Todt, whose father Jean is head of the sport's governing body and a former Ferrari boss, Leclerc is already seen as a future champion.
"I think the hype is absolutely justified," Vettel told reporters in May. "If there's no hype around him, then I don't understand who should be hyped because you walk through all the categories like that, then you belong here."
(Reporting by Alan Baldwin in London, editing by Peter Rutherford and Sudipto Ganguly)
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