"Darren has been a great servant to Connacht over the past eight years and we will be sorry to see him go.
"He enjoyed some great highlights down through the years and his hat-trick of tries in the Celtic Cup semi-final against Edinburgh will long be remembered.
"He has been with us as the professional game developed and I would like to thank him for his great contribution down through the years," Kelly said.
Yapp, who was drafted into the side by coach Steph Nel in 2000 and who has captained the side on five occasions, follows in the footsteps of Matt Mostyn who will also retire at the end of the current campaign.
The 33-year-old Yapp said: "I've had eleven great years of professional rugby and have been proud to have been with Connacht for eight of those years.
"It has been a fantastic place to work and it's been great to be a part of professional rugby during a time when the sport has grown to a point where its profile has reached such great heights, however I feel like it's the right time to retire," added the centre-cum-winger, who made his debut for the province in 2000 against Neath.
He will step down at the end of the season but hopes to stay involved in the game.
"I'd love to stay involved with a team. I'm not looking at coaching rugby at the moment but it's something I would be interested in further down the line.
"Over the last year and a half I've been doing a diploma in Health and Physiology which I'll be finishing soon but I'd love to stay involved with rugby to some degree.
"Further to this course I'll be looking to get into sports therapy and massage and am looking forward to still being involved with sport and hopefully that'll be in Galway."