An interim chair was to be appointed "in the coming weeks".
Among Mr Peters' claims were $360,662.90 paid to a bakery over two years for property maintenance, $250,000 to two firms unqualified to give financial advice and payments to a security systems company that does not exist.
Mr Robson confirmed last week that the the trust's employment investigation was looking into misuse of funding and confidential information. It is believed the suspected breaches are related.
He said the issues were historical, some dating back to 2012. If the investigation found possible criminal actions, police would be brought in.
The Health Ministry undertook a financial review of the trust in March and a governance review this month, after concerns were raised last year.
"The reviews didn't raise any specific concerns about their financial practices, but the auditors identified there was a lack of expertise at board level," said Jill Lane, the ministry's national health board director.