Strauss, who played under the Edinburgh head coach Alan Solomons at the Southern Kings, has made 56 appearances in Super Rugby with the Cheetas, Sharks and Southern Kings.
The two-time Currie Cup winner and Super Rugby semi-finalist has also represented South Africa Sevens and played for the Springboks against the Barbarians in 2010.
Subject to a medical, Strauss, whose brother Richardt plays for Leinster and Ireland, will train with his team-mates on Monday.
Strauss, who played with Edinburgh team-mates Willem Nel and Izak van der Westhuizen for the Cheetahs, said: "I'm very excited to be here. I said during the world sevens series that, if there was a city in the UK that I'd like to play rugby in, then it would be Edinburgh, so I'm very happy to get this chance in one of the best cities in the world.
"I've spoken a lot to my brother Richardt about the strength of the RaboDirect Pro12 and Heineken Cup and how they compare to Super Rugby so it's a massive opportunity for me to experience a different side of the rugby world.
Solomons said: "Strauss is a very mature player with a lot of experience. He did a fantastic job as captain for the Kings. He's a big boy, is genetically strong and his conditioning is superb. He's a natural athlete in that sense and will make a valuable contribution to Edinburgh Rugby, both in terms of playing and leadership.