Twitter released a blog post announcing Accessible Images for Everyone. The post explains, "Starting today, people using our iOS and Android apps can add descriptions — also known as alternative text (alt text) — to images in Tweets," and goes on to describe how to enable the new feature.

“We applaud Twitter’s access efforts. Tens of thousands of people who are blind or visually impaired use Twitter every day, and they will be excited to use and benefit from this increased level of accessibility,” says Lee Huffman, AccessWorld Editor and Manager, Technology Information.
Note that you must update your iOS and Android apps to access the new feature, and then enable it within your app's accessibility settings.
We hope that Twitter will move quickly to make this the default setting, instead of something that has to be enabled user by user. And we're also looking forward to seeing alt tags enabled on the web platform itself, which apparently is coming soon.

Thank you, Twitter, for making your platform more accessible to everyone!