After finding out that the main thing I used my Fitbit Charge HR for was exactly this and the Fitbit breaking after 18 months because it's not well made I got a Xiaomi Band 2 which can be obtained for ~$US 20 and it does the vibrating alarm well.

It doesn't wake me up only in light sleep rather than REM, but other than that this device fits your requirements and is the cost of a good lunch.

The battery life is also a week plus.

Also I don't really care that much if this one breaks.