The 34-year-old has not played competitive rugby since leaving Western Force last summer, after three years with the Super Rugby outfit.
Sheehan will remain with the Aviva Premiership side until the end of the season.
"Having played all of my club rugby in Australia, it is great for me to be able to go overseas and experience a different league and a different brand of rugby," he told BBC Sport.
"Since the move was suggested to me, I have been impressed with what Dai Young and his team are doing at Wasps."
Sheehan won the last of his seven Wallabies caps against Italy in November 2012.