Gibson was the launch editor of the Guardian's dedicated mediaguardian section and has been a vocal ambassador for the brand over the years.
She was among 26 people to apply for the job, and was one of just four leading internal candidates to take part in a hustings event for the editor-in-chief role.
Incoming editor-in-chief, Kath Viner, received 438 first-choice votes, 53 per cent of the total cast. Gibson came third, behind Emily Bell with 175 votes.
Gibson has announced no immediate plans about where she will work next.
A Guardian spokesperson said: "We can confirm that Janine Gibson is leaving the Guardian. It is entirely amicable and we wish her the very best for the future."
Gibson has held many roles during her time with the Guardian, including as launch editor of Guardian US, editor of Guardian.co.uk, editor in chief of Media Guardian and G3 editor.
At the Guardian US, she helped the operation grow from six employees and seven million users to 50 staff and more than 20 million users in three years.
In an internal email to staff, Rusbridger praised Gibson's "clear sense of where the Guardian should be going and what it should be in America... She's been a brilliantly talented and lovely colleague, and we wish her so well in whatever she does next."