A new register of interests will also be created for staff and contractors as part of a bid to increase “openness and transparency”.
Tánaiste (Irish deputy prime minister) Micheál Martin described the actions as “first steps towards helping restore public confidence in RTÉ”.
“As the national broadcaster, which rightly challenges other institutions, RTÉ must be leading out in terms of equality and inclusion,” he said.
Mr Bakhurst also recognised the effect the controversy has had on staff at the organisation after meeting them earlier on Monday.
“[Staff are] angry, embarrassed and rightly appalled by some of this behaviour and I share all those sentiments,” he told the News at One programme.
“My role now is to rebuild confidence and trust, and make this a much better place for people to work, a much fairer place for people to work.”
The shake up comes after Taoiseach (Irish prime minister) Leo Varadkar said trust in the broadcaster cannot be restored without change.
On Saturday, Mr Varadkar said he was aware changes to organisation were coming once Mr Bakhurst took up post.
He also stated reform of the TV licence was “long overdue”, and wanted it to happen during the current government term.
On Sunday, RTÉ’s director of strategy, Rory Coveney, resigned from his role with immediate effect.