The 23-year-old, who can operate at both full back and fly half, will add significantly to the firepower at Cardiff Blues as he links up once again with Head Coach Danny Wilson.
Morgan, who was part of the Wales squad for the 2015 Rugby World Cup and started the pool fixture with Fiji, already has five international caps to his name.
The Swansea-born back is currently in his second season at Bristol Rugby, where he has amassed 167 points in 28 matches. He was named the Greene King IPA Championship Player-of-the-Season in his debut campaign in England.
Morgan, also capped for Wales at Under-18 and Under-20 level, has previously played for Bridgend, Swansea and Ospreys, where he made 66 appearances and scored 325 points.
Head Coach Danny Wilson hailed the signing as a major boost for the attacking options at Cardiff Blues and said he was thrilled to once again get the chance to work with Morgan.
"I'm absolutely delighted to sign Matthew and to welcome him to Cardiff Blues from next season.
"Matthew offers a huge attacking threat and I'm sure the playing surface at BT Sport Cardiff Arms Park will be well suited to his game.
"I've worked with Matthew before and know what a dedicated and committed professional he is. I'm sure he will want to have a big end to the season with Bristol Rugby and then make a successful return to Wales."
Matthew Morgan said: "I'm very proud to be joining Cardiff Blues and feel I can test myself and develop the skills I need to keep knocking on the door for Wales, an ambition I'm working towards every day to fulfil.
"I want to thank Andy Robinson for the opportunity he gave me at Bristol, and Warren Gatland for the opportunity he gave me during the World Cup, two experiences I've hugely enjoyed and learnt from.
"I also want to reassure fans of Bristol that I'll do everything I can to support the club from now until the end of the season. I've had a number of offers from England, France and Japan, but felt moving back to Wales was the correct decision to achieve my goals at this point in my career."
Factfile:
Full name: Matthew James Morgan
Born: April 23, 1992, Swansea, Wales
Major teams: Bridgend, Swansea, Ospreys, Bristol Rugby
Position: Fly half/Full back
Height: 5ft 8in
Weight: 161lb
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