"He's always been a natural leader. When someone like him -- who already dipped his feet into cricket administration four or five years ago -- takes over as president of the BCCI, it's a win-win for Indian cricket.
"These are difficult times for the Board and there's a lot of work to do to bring BCCI back on the path of glory. I wish him all the best in his stint," he added.
Shastri also backed Ganguly's view of BCCI getting its dues from the International Cricket Council (ICC).
Ganguly, who was formally elected as BCCI's 39th president on Wednesday, said that BCCI is supposed to get $372 million from ICC in the next five-year cycle.
"Now, the question we should be asking ourselves is 'Is India getting a fair return for what it brings to the table?' I don't think so, and in that, I guess lies the answer. I'm pretty confident our administration is now in capable hands and they know what to do," he added.
The Indian head coach also slammed those raising questions on the lack of clarity over M.S. Dhoni's future, saying the former skipper has earned the right to retire from the game when he wants to.
"Half the guys commenting on M.S. Dhoni can't even tie their shoelaces. Look at what he's achieved for the country. Why are people in a hurry to see him off? Maybe, they don't find enough talking points," Shastri said.
"He and everybody who knows him know he'll be going away soon. So, let it happen when it has to. Making statements at his expense is downright disrespectful. After 15 years of playing for India, wouldn't he know what's the right thing to do?
"Let me say this: M.S. Dhoni has earned the right to retire when he wants to. And let this debate end once and for all," he added.
The head coach also expressed jubilance with the way Rohit Sharma performed in his debut series as Test opener against South Africa.
During the three-match Test series against the Proteas which India won 3-0, Rohit scored 529 runs -- including two centuries and a double hundred -- in the four innings he played and shattered many records.
"What Rohit Sharma has managed in this series is phenomenal. He took complete control. When someone like Rohit finds this kind of confidence in a format, I'll only say this: 'Any opposition will be wary'. He's potentially in the space that Virender Sehwag once occupied," said Shastri.
"His ability to convert 100s into 200s is something we all know. At the top, if someone like Rohit finds his feet in Test cricket, and with a beast of run-maker like Virat (Kohli) to follow, what else can a team ask for?" he added.
The 57-year-old also pointed out that the National Cricket Academy (NCA) is the most important institution in BCCI and it needs to be in the best possible functioning mode at all times.
"It is the ultimate preparatory school. With someone like Rahul Dravid at the helm there, I expect no less. We've been communicating a lot and I'm sure good things are waiting to happen," said Shastri.
"With Sourav as president and Rahul at NCA, what better combination can Indian cricket ask for?" he added.