Adams, who is paid £320,000 a year, will leave the corporation in March 2014 without any severance pay.
Adams was heavily criticised by MPs last month over large severance pay-outs given to BBC senior staff, which often breached the corporations own guidelines.
She personally authorised many of the biggest deals, including a £1.2 million payment to former deputy director-general Mark Byford and a £375,000 payoff to director of archives Roly Keating.
At her appearance before the select committee last month she admitted she felt "uncomfortable" with the huge sums, but defended herself by saying they were in line with "customary practice" and the "pervading culture" of the BBC.
In a statement, Adams said it had been "a great privilege to lead the BBC's People division" and that she had been planning to leave "for some time".
"By next spring I will have been at the BBC for five years, which feels like a good time to try something new," she said.
Tony Hall, the BBC's director general, said he would be "very sorry to see her go next spring".
Adams was previously director of HR at international law firm Eversheds, prior to that she spent nine years at Serco starting as change director in the rail division before becoming the group HR director.