Srinivasan has been suspended as Board of Control for Cricket in India (BCCI) president by India's Supreme Court after being named in the IPL spot-fixing investigation.
BCCI secretary Sanjay Patel said Srinivasan's unanimous election as the ICC chairman will be key as India take the leadership position in world cricket.
"The responsibility of guiding the game in these challenging times could not have found a better leader than Srinivasan. The BCCI wishes to congratulate Srinivasan on being unanimously elected as the first chairman of the ICC for the period 2014-2016 of two years, post its historic restructuring," said Patel in a statement.
"The restructuring of the ICC was an elaborate process undertaken by its Board and had been discussed in great detail at various levels within the ICC. It is a proud and historic moment for Indian cricket, and on behalf of all the members of the BCCI, we wish him (Srinivasan) all the best," said Patel.
Patel said that Srinivasan's election establishes the important role that the BCCI will essay and the responsibility it will take to work with other members during these days of growth.
"It is also imperative that all the stakeholders of Indian cricket stand united and support these endeavours, as we seek to play an important and definitive role in world cricket," he said.
Srinivasan is among 13 people named in the report of a court-conducted inquiry into spot-fixing in the Indian Premier League (IPL). Justice Mukul Mudgal headed the committee that inquired into corrupt practices in the sixth edition of the IPL last year.
Srinivasan has been suspended by the Indian Supreme Court as president of the Board of Control for Cricket in India (BCCI) and senior board vice-president Shivlal Yadav is looking after day-to-day cricket administration while India's legendary batsman Sunil Gavaskar was made in charge of the IPL.