Hunt will take a seat on the Channel 4 executive board while she leads the broadcaster's newly-integrated commissioning and content team across all platforms and services.
When she joins Channel 4 in January, Hunt will reportedly be on a salary of around £380,000, up from the £272,000 she currently earns at the BBC.
However, she will earn considerably less than the £1.14 million package received by Channel 4's former director television and content Kevin Lygo, who is now at ITV Studios.
Channel 4 chief executive David Abraham said that Hunt will bring an "extra level of ambition and experience" to the broadcaster as it learns to survive without the income from Big Brother.
"Channel 4 requires a fearless creative leader to help steer us through our next phase and Jay has demonstrated across a variety of public service genres as well as in commercial television, her appetite to challenge the status quo, create and lead change, and promote new talent," said Abraham.
Commenting on her appointment, Hunt said: "I am proud of what has been achieved on BBC One under my leadership but could not resist the chance to join Channel 4 at such an exciting time.
"David's vision for a converged creative business with real innovation at its heart is compelling. I wanted to be part of that.
"While I am sad to be leaving an exceptional team at the BBC, I can't wait to work with the commissioners and producers at Channel 4 who have delivered so many memorable programmes."
Speaking to The Financial Times, Hunt brushed off suggestions that she could struggle under the tighter financial circumstances at Channel 4. At BBC One she enjoys a massive budget of £1.113m, compared to Channel 4's £548.3m.
"My background includes working in [BBC] daytime and at [Channel] 5, so I have always believed you can make high quality television on a tight budget," she said.
Julian Bellamy, the head of Channel 4 who has been fulfilling the CCO role on an interim basis, will leave the broadcaster after unsuccessfully applying for the position.