Cook said he wanted his best players to be with him for the four-match Test series, which begins on November 15 at Ahmedabad.
"For me as captain this is the best possible outcome because we have a world-class player back in our team. It's been a difficult two months for Kevin but he's contrite and he's determined to get back to what he does best, scoring runs for England. As a captain that's all I want.
"I want him to come back in the side and score match-winning runs like he has in the past," he said.
The first Test match of the series will be played at Motera, Ahmedabad from November 15, while the second, third and fourth matches will be held in Mumbai (Nov 23-27), Kolkata (Dec 5-9) and Nagpur (Dec 13-17).