The move follows the acquisition of European Press, which owns Formula 1 Magazine, by the newly formed venture Formula One Publishing.
The company now plans to develop the title as the official Formula One publication by increasing the number of UK subscribers and widening its distribution abroad with the launch of a number of foreign language editions. The magazine’s website Formula1.com is also expected to undergo a relaunch next year.
Ecclestone, chief executive officer of Formula One Management, said he was sorry to see Rubython go, adding: "Formula 1 Magazine has established itself already as a strong title and Tom Rubython has done a super job in establishing it. I am sorry that he has moved on and wish him the best."
Ecclestone added: "We are pleased to have brought Formula 1 Magazine into the Formula One Group and we are excited about its future. We will build on the firm foundations Tom has laid to make Formula 1 Magazine an even greater success throughout the world."
Rubython, who founded the title in 2001, said he did not wish to comment on his plans when Press Gazette contacted him last week.
The magazine has caused controversy in the motor racing industry since its launch and was once branded "tasteless" by the boss of the West McLaren Mercedes team, Ron Dennis. He had objected to its coverage of engine builder Paul Morgan’s death, the reportage of the Adrian Newey case and graphic pictures of Mika Hakkinen’s accident in 1995, which the magazine had published ahead of the season-opening Australian Grand Prix.
"It is, in my opinion, tasteless, often inaccurate and not a positive reflection of Formula 1," said Dennis. "We all live from Formula 1 and there is a way to say things and tell the truth. In my opinion its way is the wrong way."
In response, Rubython called Dennis "naive" and suggested his outburst had more to do with the extensive coverage given to a court case brought when Jaguar Racing tried to poach designer Adrian Newey from McLaren.
Tom Walkinshaw, head of the Arrows team and former world champion and editor in chief Niki Lauda, last year voiced their concerns to Rubython and Ecclestone about the magazine’s coverage.