"I've been with Cardiff and the Blues since I was 17, starting with Cardiff Youth and I've had a fantastic time here," said Yapp. "It's a long time to be with one team so I felt the time was right to move on and face a fresh challenge.
"I've always liked Edinburgh as a city, as it's quite similar to Cardiff, so I'm looking forward to a new challenge and playing outside of Wales. Edinburgh have demonstrated what they are capable of in this year's Heineken Cup."
"There are many people to thank at the Blues, but David Young is the person who really developed my career and I spent most of it being coached under him.
"There have been many highlights during my time here from the EDF and Amlin Cup wins to some big Heineken Cup games."
"I've made some really good friends here as well and will miss them but I'd like to wish everyone associated with the Blues the best of luck for the future. There will be a young side here next season which promises to be very exciting."
Rees who announced he would be leaving the club in March has also joined Edinburgh. Rees joined the Blues from London Irish in 2007 helping win both the Anglo-Welsh Cup in 08/09 and the European Challenge Cup in 09/10.
He has made 97 appearances for the Blues, scoring 5 tries. He won the first of his 9 Welsh caps against England in the 2010 Six Nations and scored his debut international try against Australia in the 2010 Autumn Test series.