Kumble, 37, was Thursday named captain for the upcoming three-Test home series against Pakistan as the selectors opted to give front-runner Mahendra Singh Dhoni more experience of the five-day game.
"I guess it has come at a stage when the next guy takes over and I have to make sure there is a smooth transition," Kumble told reporters in his home city of Bangalore.
"It has come at the fag end of my career. But it has given me additional motivation to carry on and perform."
Dhoni, 26, who took over as one-day and Twenty20 captain in September, was considered the leading candidate for the Test role after senior pro Sachin Tendulkar turned down an offer from the selectors.
But the five-man selection committee, headed by former captain Dilip Vengsarkar, felt Dhoni's 20 Tests in two years left the dashing wicketkeeper-batsman too raw to assume the mantle.
Kumble, a veteran of 118 Tests, succeeds his Karnataka team-mate Rahul Dravid, who unexpectedly resigned as captain after the England tour in September for unspecified reasons.
The leg-spinner is India's most successful bowler and his 566 Test wickets are bettered only by Australia's Shane Warne (708) and Sri Lankan Muttiah Muralitharan, who had 700 wickets before the ongoing Brisbane Test.
"I am not looking far ahead," said Kumble, who was appointed only for the Pakistan series even though India tour Australia for four Tests in mid-December before hosting South Africa for three more Tests in March.
"Whatever job I have been given I have to ensure I do it well. I would like to cultivate a team ethic. I want us to be consistent like the Australians."
Kumble had captained India in a lone one-day international against England at Chennai in 2002 which his team won by four wickets.
The popular cricketer, who retired from one-day cricket after the World Cup in March, said he was honoured to be asked to lead in Tests.
"Every cricketer dreams of becoming the captain," he said. "For me it has come at a time which some people might say is late, but from my point of view it's better late than never.
"I came pretty close to being named captain a couple of times in the past when I was the vice-captain. So it wasn't so much of a surprise.
"Even if I had not become captain, I would not have really worried. But having been given the responsibility and the faith I need to ensure that I live up to those expectations and ensure that the team rallies around me.
"We have done well in Test cricket in the last three to four years and I need to ensure that we reach the next level and, to begin with, we need to do well against Pakistan."
The first Test against Pakistan opens on November 22 at the Ferozeshah Kotla in New Delhi, the same venue where Kumble took all 10 wickets in an innings against the same opposition in 1999.
The second Test will be played in Kolkata from November 30-December 4, while the third will be held in Bangalore from December 8-12.