The 20-year-old, who stands 6ft 3in and weighs 16 stone, worked his way through the age grade ranks and Academy at Dragons before securing his first professional contract.
Jones, a strong ball carrier with the ability to break tackles, was named in the Wales Under-20 squad for the Junior World Championship in South Africa in 2012.
He followed up that selection a year later with a place in the Wales Under-20 squad for the 2013 Under-20 Six Nations.
Director of Rugby Phil Davies said: "Ieuan has been a successful member of the Wales Under-20 set-up and is a real talent in the regional game.
"He is a strong young Number Eight and big ball carrier who will add both talent and depth to our squad as we look to next year and beyond.
"Ieuan has massive potential for us and so we are excited to have him join the Blues from next season."
The Aberbargoed-born back row, who has played a total of 29 games for Dragons since 2011 and scored five tries, admitted his relishing a new challenge at Blues.
"I'm looking forward to the opportunity at Blues and becoming part of an exciting and talent squad at the Arms Park," said Jones.
"I would like to thank everyone at Dragons for their support and I will be giving my all for the region for the rest of this season before I make the switch to Blues."