The stylish right-hander will play for the county club for the second half of the season as a replacement for Australia's Brad Hodge.
Sourav Ganguly asked for an immediate replacement because the middle-order batsman can take no further part in the tournament.
Experienced middle-order batsman Vangipurappu Laxman has been declared fit to play in the second and final Test against South Africa, starting on Sunday, India's chief selector Krishnamachari Srikkanth said.
India put up an imposing 616-5 declared in the first innings and then had one Pakistan wicket down for 50 runs at close on Day 2 of the second Test.
Paceman Shantakumaran Sreesanth has also been left out of the 12 as he is unwell.
Dinesh Karthik, who had a reasonably good Test series, made way for M S Dhoni in the team for the first two ODIs against Pakistan.
Centurion VVS Laxman said India are back into the second Test and have the self-belief they can win just a week after their 337-run loss in Melbourne.
Australia's callow bowling attack has tantalised with the promise of a brave new era, but faces its stiffest examination against India's veteran batsmen in the first Test in Melbourne starting on Monday.
Test batsman Vangipurappu Laxman was set to join Nottinghamshire after a three-Test series against Sri Lanka, while leg-spinner Piyush Chawla was to sign up with Hampshire. Both players have been told to avoid teams with links to the ICL.
India were dismissed for 642 in their first innings after tea on day two of the second Test against Sri Lanka on Wednesday.
India, chasing a mammoth 499 for victory, were dismissed for 161 in their second innings shortly after tea on Day 4 of the Test, giving the hosts a 337-run victory.
The four-match series could be the last Test tour of Australia for batting greats Sachin Tendulkar, Rahul Dravid, Saurav Ganguly and Vangipurappu Laxman, as well as leg spinner Anil Kumble, and they are intent on clinching their country's first series win on the game's toughest terrain.
"I can do much better than this," Laxman said after scoring his third century in the VB tri-series.