Binotto has served as Ferrari's technical director since 2016 but rumours of tension between himself and Arrivabene were rife previous year as the team's title challenge faded for the second consecutive season.
Ferrari had emerged as the team with the quicker auto for much of 2018, but mistakes by the team and the No 1 driver Sebastian Vettel cost the Scuderia points in a number of races.
In a statement, Ferrari said, "After four years of untiring commitment and dedication, Maurizio Arrivabene is leaving the team". Vettel's preference was for the team to continue with good friend Kimi Raikkonen for another season.
Gazzetta Dello Sport reported that Arrivabene's contract will not be renewed following another disappointing season, with management errors blamed for the team missing out once again to Mercedes.
Strategic blunders by the team past year only increased the pressure on a principal with little love or time for the media.
The Ferrari veteran, who has risen through the ranks to technical director and overseen a big step up in engine performance, has also reportedly been a target for rival constructors. The team finished second in the constructors' championship in his first season in charge before slipping back to third in 2016, but mounted more serious title challenges over the last two seasons.
Binotto, depicted as a tough character with a demanding work ethic, was very much a favourite of former Ferrari boss Sergio Marchionne who had earmarked the Swiss engineer for a leading role at the Scuderia before his untimely passing last summer. There has been talk of his exit for more than a year.
The Prancing Horse have opted to make the change after a tough 2018 campaign, which saw them fail to win either title despite a promising start to the campaign, with Mercedes securing a fifth successive double world championship.
Arrivabene's tenure has looked uncertain for some time, with reports as far back as October, 2017 suggesting Binotto could replace the former Philip Morris marketing executive.
Binotto will be spearheading a team also welcoming a new driver, with exciting academy product Charles Leclerc promoted to partner Sebastian Vettel this season. It remains unclear who will fill the void left by Binotto's promotion from technical director.