Devoy, a former squash champ, will also exit next month.
The Government-ordered review was critical of the commission's governance and management, saying that there was a deep divide between some staff and managers.
The review was sparked by the commission's handling of a sexual harassment case, and concluded that misconduct was not prevalent at the commission.
But it also revealed dysfunctional leadership at the organisation and said that commissioners "barely communicated with each other".
There were "deep-seated personality clashes" among the commissioners, in particular between Devoy and Rutherford.
Tesoriero, who joined the commission in September, will take over as acting head from today.
She will hold the position until three new commissioners, including a chief commissioner, are appointed.
The acting chief said she would continue implementing the recommendations from Shaw's review.
"Ultimately the new Commissioners will complete the work of implementing the review recommendations identified in retired Judge Shaw's report.
"In the meantime, everyone at the Commission is committed to begin making the changes so they can be implemented as quickly and smoothly as possible."
She paid tribute to her predecessor, whose term ended in 2016 but then had it extended until the end of last year.
"David has been a strong and active advocate for human rights over a number of years.
"David's legacy will be that he has made a difference to the lives of many New Zealanders."