The 30-year-old Western Province prop joined his new team in training for the first time on Wednesday and should be available for selection for Sunday's Zurich Premiership clash against Rotherham at Vicarage Road.
Visagie is one of the most respected front row players in world rugby and has been capped 29 times by South Africa after making his debut against Italy in 1999.
"I am so looking forward to my time with Saracens," explained the 18st prop. "I have been really impressed by their professionalism and their reputation is something to be proud of.
"I have been fortunate to have played for both a great country and province – it is something I will always cherish.
"Whilst it is hard for both my wife and I to leave behind family and friends, we are both excited by the challenge and opportunity that awaits us."
If the prop is planning to help reverse Saracens poor league form, his opening gambit would have pleased coach Rod Kafer.
Visagie arrived at 06.00 on Wednesday after a 12-hour flight from sunny South Africa and by 10.00 was out on the Saracens pitch taking part in a three-hour training session in the rain and mud.
"We've been looking for a prop like Cobus for some time," said Kafer. "When we heard he was available we acted quickly.
"He will give us a powerful edge up front, especially when he is joined by Raphael Ibanez next week."