Fernando Alonso is to leave Ferrari at the end of the season and the team will replace him with four-time champion Sebastian Vettel.
Alonso, 33, has two more years to run on his contract but he and Ferrari have agreed to separate. He is expected to join McLaren-Honda for 2015.
Red Bull said on Saturday that Vettel, 27, "advised them" he would leave.
Team principal Christian Horner said Ferrari made Vettel "a very attractive offer".
Horner also revealed that Vettel only told him of his decision to leave on Friday night, hours before the official announcement was made.
"It was last night when he sat down and informed us. All I can do is wish him the very best for the future," he said.
Vettel will be replaced at Red Bull by Russian Toro Rosso driver Daniil Kvyat.
Alonso's decision to leave Ferrari - which, like Vettel's arrival, the team have not announced - came because the double world champion lost faith in Ferrari's ability to deliver him a title-winning car. He believes McLaren and new engine partner Honda are a better bet.
"He never held back, he always pushed hard. I thank him for his commitment," said Di Montezemolo of Alonso
Ferrari has had a long-standing agreement with German Vettel that he would join them when he leaves Red Bull, who brought Vettel into F1 and took him to four world titles from 2010-13.
Vettel has had a disappointing season in 2014, out-shone by new team-mate Daniel Ricciardo, and has decided it is time to move on from the team that has backed him since he was a child.
Vettel will hope to benefit from the major restructuring that is taking place at Maranello under new team principal Marco Mattiacci.
Spaniard Alonso's departure has been assisted by outgoing Ferrari president Luca Di Montezemolo.
He asked Alonso if he could give him anything as a leaving gift. The driver, who has three times in the last four years finished runner-up to Vettel in the championship, asked to be released from his contract.
Alonso is said by some sources to have concluded a deal with McLaren-Honda.
The team have been chasing him for more than a year, through a change in team boss from Martin Whitmarsh to Eric Boullier, despite the turbulent relationship they had when they worked together in 2007.
After a disharmonious year during which Alonso badly fell out with chairman Ron Dennis, the two parties agreed to split one year into a three-year contract.
2001: Debut for Minardi at the Australian Grand Prix aged 20
2002: Became test driver for Renault
2003: Replaced Jenson Button as full-time driver for Renault. Became youngest driver ever to achieve a pole position at the Malaysian Grand Prix (22). Finished second in his home Grand Prix and became the youngest driver to win a Grand Prix in Hungary. Finished his first season sixth in the driver's standings
2005: Became world champion, ending the five-year dominance of Michael Schumacher. Season consisted of seven wins, six poles and 15 podium finishes
2006: Won the World Championship again becoming the youngest double world champion in Formula 1 history
2007: Signed for McLaren but terminated the contract after one season finishing third behind Kimi Raikkonen and Lewis Hamilton
2008-09: Moved back to Renault. Alonso finished fifth and ninth
2010: Signed a two-season deal at Ferrari. Finished second in World Championship.
2011: Signs contract extension with Ferarri.
2012-13: Finished second behind Vettel in World Championships for the third and fourth years running.
Sources say Dennis and Alonso made their peace with Alonso in a meeting this summer, although their relationship will inevitably always be cool.
And Honda are keen to have Alonso on board to lead their attempt to revive the famous McLaren-Honda partnership of the late 1980s and early 1990s with F1 legends Ayrton Senna and, initially, Alain Prost.
McLaren said they have made no decisions on their driver line-up, but, assuming Alonso joins McLaren, Jenson Button or Kevin Magnussen would be out of a drive.
Magnussen, right, has been outperforming Button, left, making it likely that McLaren will let the Englishman go
The team are believed most likely to keep Magnussen, who has begun to out-pace Button in qualifying. He turns 22 on Sunday, while 34-year-old Button is nearing the end of his career.
Dennis said of Button and Magnussen at the Japanese Grand Prix: "I understand they'd like to feel more comfortable than they do at the moment but it's just not necessary for us to take any decisions yet. We're waiting to see how things pan out down the pit lane.
"We obviously talk to any driver who could be on the market but we are very comfortable with what we've got.
"I can't see any reason to change anything at the moment."