Brown made 74 appearances for Dragons and scored five tries.
“I’ve been lucky enough to spend my entire playing career with the Dragons, something I’ve truly cherished and am incredibly proud of,” said Brown.
“I’d like to send a massive shout out to my team-mates – both past and present – and to the loyal Dragons fans for your continued, unwavering support.
“Everyone’s help and support over the years has not gone unnoticed by my family or I, and we will be forever grateful.
“Finally there is a huge thank you to the Dragons for sticking by me and supporting me while I tried my best to get this neck to play ball.”
Dragons interim head coach Filo Tiatia said: “We’re all disappointed Leon is retiring, but fully understand the decision he has now taken.
“I have enjoyed working with Leon. He’s left no stone unturned, with his dedication and professionalism, and developed as a leader in my time with him.”
