In July, the court accepted most of the recommendations of a three-member panel it had set up to look into the operations of the world's richest cricket board following a fixing scandal during the 2013 Indian Premier League Twenty20 competition.
The BCCI rejected a few of the recommendations made by the panel headed by former chief justice R.M. Lodha, which included age and tenure restrictions for top officials, as well as banning them from serving successive terms.
"One should understand that once the order of the Supreme Court, the highest court of the land, has come it has to be obeyed by all... nobody can escape it," Lodha told reporters after the verdict.
"Being at the helm of affairs, if they were not able to implement the Supreme Court order, these consequences were bound to follow and that's what has happened.
"Administrators come and administrators go but ultimately it's for the benefit of the game and the game will flourish, I'm very sure."
A senior vice president of the board will take over as the interim chief, the court added.
Shirke said he was yet to read the order but was ready to step down.
"If the highest court of the land wants me to leave, I'd leave happily, I have no issues," he told CNN News18 channel from London.
"We have to see that the BCCI, in its new form, continues to do well, cricket flourishes and India is able to maintain its position in global cricket."
India consolidated their position as the world's top-ranked test team with a 4-0 home series victory against England last month and will host them for three one-dayers and as many Twenty20 Internationals from Jan. 15.
(Reporting by Suchitra Mohanty; Writing by Amlan Chakraborty; Editing by Sudipto Ganguly)
