Wales have recorded just one win over the Boks since the dawn of international rugby and have never beaten the All Blacks in the Land of the Long White Cloud but Byrne sees the challenge as exciting rather than daunting.
"It doesn't get much tougher - the two best teams in the world - but they are the teams you want to be playing against," said Byrne, who will win cap number 33 in Cardiff on Saturday.
"There are three more games of the season left, and if we could get three victories it would be a great achievement.
"As a player, you just want to get out there and play again."
Byrne last faced the Boks for the British & Irish Lions in the summer of 2009 - a series that ultimately ended in disappointment for both the Lions, who lost the series 2-1, and for Byrne, whose tour finished prematurely due to injury.
But the former Scarlets star believes that particular experience 12 months ago could give so many of the Wales side an extra motivation, while the recent trophy-winning exploits of both the Ospreys and the Blues will give the party as a whole a huge confidence boost.
"It is the first time I will have played against them since the Lions tour," added Byrne.
"It's unfinished business, yes.
"It's going to be exciting, and hopefully we can give the fans something to cheer about.
"South Africa have left a lot of players behind, but the team they've got out on Saturday still includes world-class players throughout.
"That's a credit to them - they've got players coming through in every position - and if we get a win at the weekend it's a big statement before we head to New Zealand.
"I am sure this weekend we can take confidence after what ourselves and the Blues have achieved in the last couple of weeks.
"It seems to be every time we win a Grand Slam, the year after we end up finishing fourth, or something, in the Six Nations. We have to get out of that cycle.
"But the last game we played against Italy we showed some character, and we need to take that forward now."