We need to break this into two separate tasks: recognizing when the button has been pushed outside the home, and then creating a spoken notification inside the home.
A. Recognizing when the doorbell button has been pushed
There are three simple Z wave devices that are popular. 
A1) Nexia makes a device which is intended for use with your existing wired chime box and sending a notification to the hub when your existing doorbell button is pressed. This works very well for many people.
https://www.amazon.com/Nexia-Z-Wave-Doorbell-Sensor-DB100Z/dp/B017VVO9QQ
A2) The Aeotec doorbell can play up to 99 different custom soundtracks, so you can use it a lot of different ways. You can trigger the sounds from any smartthings – recognized event as well as from its own button. The soundbox plugs in and the button is battery powered.
So this option not only gives you a button, it gives you a way to create custom sounds that can be triggered from other events as well.
A3) The Dome chime is a simpler zwave device that can only play one of 10 pre recorded tracks.
https://www.amazon.com/Dome-Home-Automation-DMS01-Battery-Powered/dp/B01M1NLPKZ
It doesn’t come with the button, though, so you have to combine it with another Device. @Jimxenus already gave you the link to the buttons FAQ – – that has most of the possible button devices. The Aeotec panic button is popular for this use.
https://www.amazon.com/Aeotec-Button-Z-Wave-Control-Trigger/dp/B00PJ88FUA/
So that’s three different ways of approaching recognizing when someone has pushed the button outside the home.
So now you have a message sent to the hub when the doorbell is pressed. You can use that to trigger any event that smartthings can control, whether it’s changing a colored light bulb to orange, turning on the porch lights, turning on the television, etc.
However, you also asked for the ability to have Alexa playing announcement.
B. Playing spoken notifications after the button is pushed
As far as having Alexa speak a notification, that is not possible at the present time although it may be possible in the future. There are a few alternatives.
B1) The Aeotec doorbell was already mentioned in A2 above and is a good alternative for many people, but now we are looking at it as a device to play sounds on command. Again you can upload up to 99 different custom sounds to it. You will need custom code for it:
There are also people who will use this Device for the sound player, but use the Nexia sensor listed in A1) to capture the button event. That way they keep their existing doorbell hardware but still have lots of sound notification options.
B2) The LANnouncer approach that was already mentioned can work with an android device, although set up is fairly complex. It’s popular for people with strong technical skills.
B3) Another popular option is to use any text to speech (TTS) speaker and have it set up to “notify with sound.” People use these for everything from dogs barking to spoken announcements. These will be easy to use with SmartThings, it’s just that the speakers themselves can be pretty expensive. 
Here is the official support article on “speaker connect” which is the official feature for using this type of speaker.
https://support.smartthings.com/hc/en-us/articles/115002004243-Speaker-Companion
Using it is very similar to using the official smartlighting feature, except instead of having lights come on you are having sounds play. But again you have to have a speaker Device that has this ability and right now echo devices don’t accept this kind of command.