Srinivasan, 68, widely regarded as the most powerful man in world cricket, had been barred by the court from taking charge since his election on September 29 as chief of the Board of Control for Cricket in India (BCCI) for a third year.
"Srinivasan can take over as BCCI president, but we have also formed a new probe panel to investigate the case," ruled A.K. Patnaik, one of the two judges who heard the case.
The court appointed a three-member panel headed by a former judge to investigate a scandal that has rocked the popular Indian Premier League (IPL) Twenty20 tournament run by the BCCI.
The probe will be separate from investigations by police, who have filed charges in court against a string of officials, players and bookmakers for illegal betting on the IPL.
A cricket body in the eastern state of Bihar which is not affiliated to the BCCI had petitioned the court to prevent Srinivasan's return on moral grounds because his son-in-law had been charged in the scandal.
The son-in-law, Gurunath Meiyappan, was the team principal of the Chennai Super Kings, the IPL franchise owned by Srinivasan's India Cements company and captained by national skipper Mahendra Singh Dhoni.
Srinivasan, who has not himself been accused of any wrongdoing, stepped aside temporarily as BCCI president in June when Meiyappan was named in the scandal.
The new Supreme Court-appointed panel, whose expenses will be borne by the BCCI, was given four months to submit its findings to the court. The verdict came after Srinivasan agreed not to interfere in the panel's working.
"Srinivasan has himself made it very clear that he would not be involved in the investigation of IPL match-fixing allegations," BCCI lawyer Aryama Sundaram told reporters outside the court.
The BCCI's head of operations, Ratnakar Shetty, welcomed the Supreme Court's decision.
Srinivasan's immediate task will be to finalise the schedule for next month's tour by the West Indies for two Tests and three one-day internationals. (AFP)
