The Italian team, the sport's most successful and glamorous, said the new deal covered the 2018, 2019 and 2020 seasons but gave no further details in a statement of just 30 words.
There will be inevitable questions about possible release clauses, not to mention speculation about how many tens of millions of dollars the 30-year-old German will be earning over the period.
But the news, at the Belgian Grand Prix and a week before his team's home Italian race at Monza, will allow Ferrari to concentrate on fighting for the championship without distraction.
"I love this team. I love the people who are working for this brand," Vettel told reporters later.
"Ferrari has something unique, something that other teams don't have. People talk about a legend. To me it appears that this legend is still alive because of the people who work for it, day in, day out.
"In a way, it was a no-brainer to continue. We haven't yet achieved what we wanted to achieve but things are looking pretty good, and obviously we have a long road ahead of us," he added.
The four-times champion, who joined Ferrari from Red Bull in 2015, is 14 points clear of Mercedes rival Lewis Hamilton in the current standings with nine races remaining.
The German had been out of contract at the end of this season and there had been speculation about a possible switch to Mercedes -- a move that would have sent a tremor through the paddock.
Hamilton, a triple world champion who has one more year left on his Mercedes contract, laughed off that possibility earlier in the week when he told reporters that his rival did not want to be his team mate.
Niki Lauda, the Mercedes non-executive chairman, told Sky Sports that there had been talks with Vettel but team principal Toto Wolff said that was not the case.
Vettel's Finnish team mate, Kimi Raikkonen, the 2007 world champion, has already agreed a contract extension for 2018, keeping Ferrari's line-up unchanged for next year.
Raikkonen, 37, and Vettel get on well, with the Finn playing the role of loyal sidekick to the team's main championship contender.
Mercedes are now likely to retain Finland's Valtteri Bottas, who joined in January from Williams as a replacement for now-retired 2016 champion Nico Rosberg on a one-year deal with options.
That will put the main focus on McLaren's Fernando Alonso, who is also out of contract and looking for signs that the team can provide him with a competitive car before agreeing any new deal.
The Spaniard, a double world champion who raced in the Indianapolis 500 this year, would appear to have limited options within Formula One although he said he had received several offers.
Reporting by Alan Baldwin, editing by Clare Fallon, Neville Dalton