The 33-year-old leg-spinner, who missed the preceding One-day series due to a shoulder injury, will spearhead India's bowling attack in the three Test matches starting on Sunday.
"It's great to be back in the fold," said Kumble, India's most successful spinner with 382 wickets from 81 matches.
Kumble emulated Englishman Jim Laker when he grabbed all 10 wickets in an innings during the second Test against Pakistan at New Delhi in February, 1999.
"I am on my first tour of Pakistan and look forward to playing," he said on Friday. "It is going to be very challenging series. I think the boys were brilliant in the One-day series and we can take a lot of positives from that going into the Test matches."
India came from a 1-2 deficit to win the One-dayers 3-2 following a 40-run win in the decisive fifth match at Lahore on Wednesday.
"It was a wonderful show by the team to win their first One-day series ever in Pakistan. I hope we can do the same in the Tests." India have never won a Test match in Pakistan on five previous tours comprising 20 Tests. The hosts won five Tests while the rest were drawn.
"It is an education for international cricketers to play in different conditions around the world," Kumble said. "We had a very good tour of Australia where we held the world champions to a 1-1 draw in the Test series.
"The conditions will be different in Pakistan from what we had in Australia, but that tour gave us the confidence to play well anywhere."
Kumble reckoned the pitch at the plush Multan cricket stadium appeared to be "a good Test wicket" and hoped he will be able to extract good bounce from it. "Pakistan has always been a strong opposition and will be an even bigger threat playing at home. But hopefully we will play to our full potential and win," he said.
Kumble goes into the first Test without a first-class game since January 6, the last day of the fourth and final Test against Australia at Sydney.
"I am not worried about the lack of match practice," he said. "I should be able to adjust to the conditions quickly since they are quite similar to what we get at home."