The 23-year-old back will leave Bristol at the end of the season in May.
"I had a number of offers from England, France and Japan, but moving back to Wales was the correct decision at this point in my career," said Morgan.
"I feel I can test myself and develop the skills I need to keep knocking on the door for Wales."
Newport Gwent Dragons were also keen to sign Morgan, who can play at full-back or fly-half, and started against Fiji in last year's World Cup.
He is in his second season at Bristol and has scored 167 points in 28 appearances for the Championship side he joined from Ospreys in May 2014.
Morgan was named Championship player of the season in his debut campaign in England.
Blues head coach Danny Wilson worked with the player at Bristol and with Wales under-20s and expects Morgan to play most of the time at full-back.
"He has the ability to cover other positions but it's primarily full-back that we have recruited him for," said Wilson.
"It dovetails in with what Wales have done with Matthew recently. Matthew on our (artificial) surface (at the Arms Park) will be a real threat with his footwork and his ability to beat defenders."
Morgan played 66 games for the Ospreys but found his game-time at fly-half limited by Dan Biggar and the emerging Sam Davies, prompting his move to Bristol.
Matthew Morgan says he turned down offers from around the world to join Cardiff Blues in the pursuit of adding to his five Wales caps.