Cohen was responsible for commissioning shows including Call The Midwife, Poldark, Last Tango In Halifax, Happy Valley and Car Share.
"After eight wonderful years at the BBC, it is time for my next big challenge," he said.
"In the last few weeks I've been approached about a number of exciting opportunities and I want to consider these in an open and transparent way."
Cohen joined the BBC from Channel 4 in 2007 and went on to become BBC One controller in 2010. He was promoted to the director of television post three years later.
His job involved dealing with a series of high-profile disputes and criticisms.
He took the phone call following Jeremy Clarkson's assault on a Top Gear producer, which led the presenter to leave the corporation.
He also apologised to Sir Tom Jones after the singer complained of "sub-standard behaviour from the executives" when he was sacked as a judge on The Voice.
And he faced strong criticism this summer after asking celebrities to sign a letter supporting the BBC as it negotiated with the government over the future of the licence fee.
In a statement, Cohen said: "BBC Television is on brilliant creative form. I feel very privileged to have led Television for the world's finest public service broadcaster and to have worked with so many smart and talented people.
"I'm very proud of the wide-ranging success of BBC Television under my leadership. There has never been a more exciting time for television and digital media.
"I'm looking forward to taking up a new leadership role in this age of intense creative and technological innovation."
Cohen will leave at the end of November. His new job has not been announced.
In August, he admitted that the BBC could not compete with the finances of Netflix, which meant the streaming service turned down the corporation's offer to co-produce new royal drama The Crown.
The Guardian has reported he is "considering offers from both UK and US companies".
BBC director general Tony Hall described Cohen as "one of TV's great talents" who had done "an extraordinary job" in his time at the BBC.
"In a world of intense competition and choice, he has further enhanced the BBC's reputation for quality programming that is full of ambition and creativity," Lord Hall said.
The BBC's director of television Danny Cohen is to leave the corporation.