He had been unable to hold down a starting place in the Edinburgh front row after joining from Cardiff Blues a year ago, though he made a total of 23 appearances.
Yapp, who has earned 21 caps for his country and was part of the Wales squad which won the RBS 6 Nations in 2005, couldn't disguise his delight at the move to Reading. "London Irish proved during the second half of last season that they are a very good side and I am looking forward to playing in the Aviva Premiership," he said.
"It is a difficult competition with some fantastic players. As a player you want to test yourself against the best week-in, week-out and I will be able to do that with the club."
Brian Smith, the London Irish manager, said: "I have been very impressed with John throughout his career, especially on the international stage. He is a loosehead prop with significant experience, and his power, knowledge and tenacity will really strengthen our front row."
Glenn Bryce, a full-back, has followed another Scot, Colin Philips, in moving to Doncaster Knights. The 22-year-old, who learned his trade at Stirling County and Heriot's, was one of Jersey's first full-time professionals when he joined in 2011 and went on to play a major role in their promotion to the Championship, the second tier of English rugby.
Knights are in National One, the third tier, and Bryce, brother of new Glasgow Warriors man Kevin, said: "Promotion is obviously the ambition for everyone associated with the club. I know that won't be easy and a lot of teams will want to raise their game when they play us, but I'm looking forward to taking the challenges on. I'm very excited about my move to Doncaster."
Philips, a prop who played for Scotland Under-20s at the same time as Bryce, has played for Stewart's-Melville and Currie in Scotland before having a stint in Ireland. He joined the Yorkshire club a couple of weeks ago.