The 30-year-old, a former Cardiff Blue, has been part of a Wasps side that have been pushing for the top six in the English Premiership.
Meanwhile Dragons have struggled this year domestically, ending a run of four straight defeats last time out against Munster but remaining second bottom.
But with Thomas on board Edwards is confident he and his players have an example to lead the region moving forward.
"Rhys will be a great addition to our pack of forwards, he brings with him a wealth of experience," said Edwards.
"I am confident he will make a difference on the field and also be a great mentor for our other hookers and young players."
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