Indeed Jones has made just seven appearances for the Dragons this term and instead will turn his attentions to helping Bristol into the English top flight and Beale was quick to wish him well.
He said: "We would like to thank Matthew for his contribution at the Dragons and wish him luck for the rest of the season and the future."
Bristol are currently top of the English Championship and Jones is relishing his new challenge on the other side of the Severn.
"I'm pleased to be joining Bristol Rugby," said Jones. "The club are enjoying a strong season and there seems to be a fantastic team spirit.
"I'm looking forward to competing in the Championship and challenging for a spot in the first-team."
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