Shastri was yesterday appointed coach, filling in the void left by Anil Kumble's resignation last month.
The 55-year-old former skipper sounded upbeat about the times ahead.
"It can be a better Test team than any Indian team we have had. This is a team you can travel with (anywhere). There is a battery of pacers which can do well in all conditions and take 20 wickets. Their age is such that they are playing at the right time," Shastri told 'India Today' from London.
"Kohli is a champion cricketer, he has not yet reached his peak. The next five or six years will define the real Virat Kohli," Shastri said.
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Asked about seasoned campaigners Mahendra Singh Dhoni and Yuvraj Singh's future, Shastri said, "2019 (World Cup) is a long way to go. They are both champion cricketers. We will deal with it when the time arrives. I am just getting into the dressing room again, so I need to spend time with the captain (Kohli) and take things forward."
"I have always relished a challenge and I am looking forward to my stint with India. When you are asked to open the batting in overcast conditions, it is a challenge. I am used to challenges, bring on another one," Shastri said.
Asked about his frosty relationship with Sourav Ganguly, a member of the Cricket Advisory Committee (CAC) that appointed the coach, Shastri played down the bitter spat.
"We are both former captains and there will be arguments, but we need to look at the bigger picture. He (Ganguly) asked some very good questions during my interview. We need to move on. Individuals don't matter, and we should all work in the best interest of Indian cricket. It should take the centre- stage.