"This is a decision taken jointly by ourselves and Sebastian, one which both parties feel is for the best," team principal Mattia Binotto said in a statement.
"It was not an easy decision to reach, given Sebastian’s worth as a driver and as a person."
Vettel, who joined in 2015 with the dream of emulating boyhood hero Michael Schumacher in winning titles with the sport's oldest and most glamorous team, is out of contract at the end of the year.
Where the 32-year-old German will go now, and indeed whether he will remain in a sport whose delayed season has yet to start due to the Covid-19 pandemic, are the big questions.
"The team and I have realised that there is no longer a common desire to stay together beyond the end of this season," Vettel said.
"Financial matters have played no part in this joint decision. That’s not the way I think when it comes to making certain choices and it never will be."
"What’s been happening in these past few months has led many of us to reflect on what are our real priorities in life," he added.
Vettel said he would now take time "to reflect on what really matters when it comes to my future".
German media, who flagged up the departure on Monday night, reported Vettel had rejected the terms being offered by Ferrari.
Italy's Gazetta dello Sport newspaper recently reported Vettel, who won 14 races with the team and is their third most successful driver, had been offered a one-year extension with a salary reduction.
The German, who won his titles with Red Bull, told reporters last month he could have a new deal done before the start of a season delayed by the coronavirus outbreak.
Ferrari had also said the German was their first choice to partner Charles Leclerc.
Binotto said there was no one reason that led to the split "apart from the common and amicable belief that the time had come to go our separate ways in order to reach our respective objectives".
Leclerc, who won two races last year and is only 22, has a contract until 2024 and is seen as Ferrari's future and likely first champion since Kimi Raikkonen in 2007.
The Monegasque outperformed Vettel last year in his first season at Ferrari, finishing ahead of him overall and taking more points, poles, podiums and wins.
Australian Daniel Ricciardo, at Renault, and McLaren's Spaniard Carlos Sainz have been installed as the leading candidates to take one of the most coveted seats on the grid.
Six-times world champion Lewis Hamilton has also been linked to Ferrari but has repeatedly indicated he intends to stay with Mercedes.
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