If so, how do you announce it in a newsletter without it looking like spam to them?
What's the time differential? If it's a logical next step, it's probably ok. If it's a complete shut down - or an asset sale (which would mean that the email list is owned by the acquiring company) - or longer than say 4-6 months, I would say no.
That being said, if you are in the process of shutting down the first company, there is nothing wrong to asking your users if they are open to hearing more in the future.