The money was shifted over an eight-year period but the National Bank, now part of ANZ, has not disclosed how the offending went undetected for so long or how Cooper was eventually found out.
Cooper owns two houses in Auckland which have mortgages with ANZ.
Property records show his wife and a trustee company in Henderson, Davenports West Trustee Company, are also listed as owners.
The second house was bought in 2008 for nearly $330,000, and it is understood the money-laundering charge relates to this deal.
Cooper will be sentenced in the Auckland District Court in June.
He is expected to receive a prison term shorter than that of another personal banker who stole $17.8 million. Stephen Versalko was jailed for six years in 2010 after admitting a long-running fraud which he used to fund a lavish lifestyle.
An ANZ spokesman said the bank found a discrepancy and told police.
"This was sophisticated offending by someone who had knowledge of our systems and processes and was trusted," the spokesman said.
"Many staff and customers feel extremely let down by this person."
He said the bank had reviewed its systems and more robust security measures were now operating.
Graeme Malcolm Cooper
• Former personal manager for National Bank.
• Pleaded guilty to 41 criminal charges including accessing a computer system, use of documents for pecuniary advantage and money laundering.
• Crimes had four victims.
• Total fraud was nearly $1 million.
