Maurizio Arrivabene has been replaced as Ferrari team principal by former technical boss Mattia Binotto.
Arrivabene had held the role for four years and a Ferrari statement said the decision was made by "the company's top management after lengthy discussions."
Binotto takes immediate charge and Ferrari said "all technical areas will continue to report directly" to him.
Ferrari failed to win either title in 2018 amid a series of driver and management errors.
Arrivabene, 61, had been boss of the team since December 2014, joining from main sponsor, the tobacco giant Philip Morris, where he was a vice-president.
He was in charge of Ferrari while the team enjoyed a revival in competitiveness in the last two seasons.
But he was widely seen within F1 as a Ferrari figurehead only, with the real power instead resting with former president Sergio Marchionne, who masterminded a reshuffle of the technical department in 2016 but died from complications during surgery for cancer last July.
Marchionne's intention before his death had been to remove Arrivabene and replace him with Binotto, who had led the team's technical department to a series of widely copied design innovations since 2016.
Following Marchionne's death, there was known to be a power struggle between Arrivabene and Binotto.
Binotto, 49, had been approached by other teams, and new Ferrari chairman John Elkann decided that continuing with Marchionne's plan was the best option.
Nevertheless, Arrivabene's departure just two months before the start of the new season on 17 March will inevitably raise questions as to how the change will affect the running of the only team that has been able to regularly challenge world champions Mercedes in the last two years.
Ferrari's failure to win the title last year was largely down to mistakes from lead driver Sebastian Vettel, and failures of operational management, for which Arrivabene had overall responsibility.
Under Arrivabene, Ferrari had undertaken an internal review into the failure of 2018, the conclusions of which were that the fundamental problem was that they needed a faster car to deliver on their ambition of beating Mercedes to the title.
Additionally, they concluded that Vettel's errors came from the driver feeling he needed to push harder than he would have liked to in order to make up for the car's shortcomings.
It is an interpretation that is open to question given that Ferrari and Vettel squandered a series of opportunities that, had they seized all of them, could have seen the German beat Mercedes' Lewis Hamilton to the title.
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What will Binotto bring to the role?
Arrivabene's stewardship of Ferrari was characterised by an almost total lack of communication with the outside world.
He ceased the common practice of doing regular media briefings at every race, and his mandatory appearances in official news conferences at races were often characterised by a combative and dismissive attitude to questions.
As such, Arrivabene operated a management style that was very different from his counterparts at the Mercedes and Red Bull teams, Toto Wolff and Christian Horner.
Binotto is highly regarded as an engineering leader. Insiders say he has a good, rounded view of the business of F1 in Ferrari, but may need some help on the commercial side of the company.
This will include the relationship between Ferrari and the F1 Group at a critical time over new contracts to replace the existing ones between the teams and the sport that run out at the end of 2020. Discussions over a new commercial relationship and changes to the technical rules have been ongoing for some time with no conclusion.
As such, some say, he shares some of the characteristics of former Ferrari technical director Ross Brawn, another engineer who became a manager and then a team principal.