Stoddart said: "It is with real sadness that I have to announce my retirement from rugby and it has been a difficult few months as I come to terms with the fact that I was not going to return to full fitness. I have been very fortunate to play for the Scarlets and Wales and have enjoyed every game in my professional career working alongside some brilliant fellow professionals.
"I worked as hard as possible in the year I was off to get back on the pitch and that can be a difficult period for any injured player mentally, as well as physically, but I was determined to get back to playing.
"But ever since I've been back on the field I've had significant pain in the leg throughout and that has not improved. Following a series of medical tests and consultations, detailed scans and strength tests, I've been advised that I cannot continue."
Stoddart said it was tough to have to give up his rugby career but easier to an extent because the choice was taken out of his hands. "It's not easy to give up your rugby career but when it really is impossible to carry on you just have to accept it and get on with it.
"I have some great memories that I will never forget and the Scarlets and all our supporters have been fantastic over the years. It was an honour to play in the Scarlets shirt, with all the great names that have been part of our region throughout our history and a pleasure to play in front of our Scarlets supporters who are the life and soul of our region.
"I will miss all the spirit and passion of Scarlets rugby and the level of commitment and hard work the players put in for our region and its supporters of which I have been proud to have been a part.
"I'm grateful for all the great opportunities and experiences I have had in my rugby career and there are many brilliant memories including the Heineken Cup with the Scarlets and playing for my country."
Scarlets Head Coach Simon Easterby, added: "It is very disappointing for Morgan and for all the Scarlets team and our supporters to see a player of his ability and quality forced to retire early.
"He's been a player of real class and quality within our regional ranks ever since he joined the Scarlets and a player that you can rely on to make a difference in games and give you an edge. He has worked so hard to try and recover from this horrific injury and credit to him for even getting that close, that shows his great mental strength and commitment.
"We are very sorry to see him go and every one of the team and I am sure all our supporters wish him all our very best in his future life off the field and as Scarlets we will support him as much as we can in whatever he chooses to do."