It's almost 2018 folks and the idea of announcing the launch of a new website is rather passé. This is because updating your website redesign is something that people expect to occur. And they expect it to occur often.
As a marketing agency, we encourage our clients to constantly think about the next step. With respect to your website redesign, that next step is called iteration. It's part of what we preach under the Growth-Driven Design philosphy.
People don't give you their email address because they want to keep up with the monthly goings-on of your business; they sign up for your email list because they think you're going to offer them something of value. A pretty, new website is quite honestly a bit self-serving and mostly valueless to your customer. Always try to stand in the shoes of your customer.
An offer would be nice. Offers are always a good reason to send an announcement to your email list. Create an offer that requires customers to visit the website to take advantage of it so this they will experience the website redesign for themselves.
If you really think your new site has features that add value to your customer, then explain that feature and why it's going to make their day that much brighter. Perhaps, you have a new way to make one-stop purchases without having to fill in lengthy information each time, or maybe there's a live chat feature that helps them get answers quicker. If you think it adds value to them, then make sure they know it.
Perhaps, your previous website was from the Dark Ages and it was a real cause for previous customers to go elsewhere with their business. Use this opportunity to invite them back. Tell them that all those wonderful features that were once hidden in the bowels of the system are now upfront and easily accessible to them. Again, show and tell them the value they will experience by visiting you again. And, oh, by the way, offer them a discount to make it worth their while.
Use this opportunity to ask for feedback. Customers know what they want and if you give them the opportunity to be "beta-testers" they may gladly offer up their opinions as they see value that may benefit them down the road.
To sum it up, anything that doesn't add value to your customer's life, or requires their immediate action, will end up in the trash, or worse yet, prompt them to unsubscribe. So, always be offering value.