Srinivasan, 68, widely regarded as the most powerful man in world cricket, had been barred by the court from taking charge since his election as the BCCI chief for a third year on September 29.
"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 in the capital New Delhi.
The court appointed a three-member panel headed by a former judge to investigate the scandal that has rocked the popular Indian Premier League Twenty20 tournament run by the Board of Control for Cricket in India (BCCI).
It said the panel, whose expenses will be borne by the BCCI, had four months to submit its findings to the court. The verdict came after Srinivasan agreed not to interfere in the panel's working, a BCCI lawyer told reporters.
The probe will be separate from continuing investigations by police, who have filed charges in court against a string of officials, players and bookmakers in the scandal.
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 Bihar association had argued in court that a previous internal BCCI probe had absolved Srinivasan, Meiyappan, India Cements and other IPL officials of wrongdoing even before police had filed charges in court.
Srinivasan's hold on world cricket stems from India's vast television audience, which enables the country to generate almost 70 percent of the game's revenues.
International news organisations, including Agence France-Presse, have suspended their on-field coverage of matches hosted by the BCCI since last year after the board imposed restrictions on picture agencies.