The 32-year-old lock forward becomes the 13th player to join the Dragons, as they prepare for life in the Championship.
Leo has previously played for Perpignan, Bordeaux Begles and Wasps, while making 75 appearances in the Aviva Premiership during his time on these shores.
"Dan is vastly experienced in the Premiership, Top 14, Heineken Cup and at international level," London Welsh director of rugby Steve Lewis is quoted as saying by BBC Sport. "That experience will be hugely beneficial in next season's Championship campaign."
Leo has represented Samoa at two World Cups in the past, with the last of his 39 caps coming against England in November.