"Mr Webster's career has to date focused on enabling and driving good governance, the promotion of democratic rights and values, the development and application of codes of conduct and behaviour, and working to ensure compliance with both statutory provisions and constitutional conventions," Faafoi said.
"I am sure Mr Webster will provide the leadership required to ensure the public can be confident that their privacy rights are being protected".
Edwards, who departed after seven and half years in the role in December last year, was one of the influences behind a recent update to the Privacy Act that introduced mandatory data breach disclosure, among other measures.
While the legal powers of the role remain limited compared with privacy watchdogs in the EU and elsewhere, Edwards did not stint from using a public dressing-down to extend its influence, with Facebook a frequent target.
The Herald understands that Edwards was, at times, asked to pull his head in.
His replacement has, to date, had a lower-key career.
He starts his new role on July 5.