It varies, some accounts seem to be approved almost immediately, while others take a few days.
I think the variation has a lot to do with DreamHosts automated fraud detection system. As I understand it, certain (unknown) aspects of an application can trigger this system and the application gets flagged for manual approval, which takes time.
If your account is not approved within a day or so, a support request (sent through the panel) has been known to speed the process.
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