Renault said the parting was by "mutual consent" but Vasseur pointed to a fundamental disagreement.
"There was too much different vision in the management of the team, so at this stage I think it makes sense for me to leave," he told motorsport.com.
"If you want to perform in F1, you need to have one leader in the team and one single way. If you have two different visions then the result is that the work inside the team is slow," he added.
Vasseur's departure came a day after champions Mercedes announced the exit of technical head Paddy Lowe, who is now expected to show up at Williams after a period of 'gardening leave'.
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For the first time in 23 years, Formula One will have no reigning world champion in action as a consequence of Nico Rosberg retiring five days after winning the title with Mercedes.
The German's replacement has yet to be announced.
McLaren had already parted company with their boss Ron Dennis, while engineering head Pat Symonds left Williams at the end of last year.
Tail-enders Manor are meanwhile facing an uncertain future after going into administration this month.
Renault, who took over failing Lotus at the end of 2015 and finished ninth of 11 teams last year, are due to unveil their new car on Feb. 21 with the season starting in Australia on March 26.
The team, who have Germany's Nico Hulkenberg and Britain's Jolyon Palmer as drivers, started 2016 without a designated principal and will be run by president Jerome Stoll and managing director Cyril Abiteboul.
Vasseur, who took on his role midway through last season, has a reputation for success in the GP2 support series with his ART team.
Hulkenberg won the GP2 title with ART in 2009 and had been looking forward to linking up with Vasseur again after switching from Force India at the end of last season.
There had for some time been reports of differences of opinion among the management despite Renault, who have restructured the team and recruited more staff, setting what looked like realistic targets.
"We knew... when we took over the company that 2016 would be very difficult in terms of results. That's life. We have to build up a strong team for the future," Vasseur told Reuters a year ago.
(Reporting by Alan Baldwin; Editing by John O'Brien and Toby Davis)
