SQLSTATE[HY000] [2054] The server requested authentication method unknown to the client (no replies)

I am attempting to install Piwik for the first time and have received the following error when creating the database using PDO/MYSQL:

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Error while trying to connect to the database server:
SQLSTATE[HY000] [2054] The server requested authentication method unknown to the client
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I also receive this when using MYSQLI:

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Error while trying to connect to the database server:
The server requested authentication method unknown to the client
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How do I fix this?

- M