The 28-year-old was garnted work permit and will replace paceman Jason Gillespie, who has been called up for the Australia A tour to Pakistan.
Tahir was named in the squad for last week's Championship match against Warwickshire at Scarborough.
But he was unable to make his debut after the club learned that his work permit to play league cricket in England was insufficient.
Tahir was recommended by team-mates Inzamam-ul-Haq and Jacques Rudolph the latter having played against him in South African provincial cricket.
And he is hoping to make a positive impression at Headingley following a brief spell with Middlesex in 2003.
"I am delighted to be here and I'm really looking forward to playing for Yorkshire. The Yorkshire team is doing well this season, so it would be great to be able to play a part in finishing the season in a successful way," Tahir told the club's website.
He is likely to form a leg-spin tandem with England prospect Adil Rashid as the team tries to win the title for the first time since 2001.
Yorkshire currently hold a 14-point lead over second-placed Sussex, but must win next week's match at Hove as the south coast club have a game in hand.
English County Championship