Bezuidenhout joins the club on a high after finishing top points scorer in the Currie Cup, South Africa's premier domestic competition, which he won with the unbeaten Pumas.
The 27-year-old, who began training with the RaboDirect Pro12 club on Monday, said: "I'm extremely excited to be here.
"Playing in Europe is something I've wanted to do for a long time now, I just needed the break and this is it.
"It's a fantastic opportunity for a new experience; different rugby, different people, different cultures, it's all very appealing to me and I'm really glad I'm here.
"I've always wanted to travel with the sport. I got married in March so it's something that we both really wanted to try as well.
"It's just going to take hard work. I need to get stuck in from day one.
"Hopefully I'll get a chance out on the paddock soon to play my natural game and kick on from there.
"I'm delighted about it and want to grab it with both hands and get an extension."
Bezuidenhout has enjoyed wide success in South Africa. He helped the Natal Sharks lift the 2008 premier division title and reach the semi-finals on three other occasions before helping Pumas to a Currie Cup runners-up spot in 2012 and the title this year.
Edinburgh head coach Alan Solomons, whose team face Glasgow in Scotstoun on New Year's Day, said: "Carl has performed really well for the Pumas and played a pivotal role in their Currie Cup success this year.
"His game management is very good, he's got a good boot out of hand and for goal, and is very athletic.
"He now has an excellent opportunity to show us what he is capable of, while also solving an immediate issue in that we are desperately short of fly-halves.
"We will have to see how he tracks for us but I think he has the ability."
Solomons last week signed former England schoolboys international Tony Fenner on a one-month loan deal after Harry Leonard (thigh) joined fellow fly-halves Gregor Hunter (knee) and Piers Francis (foot) on the sidelines.