Kevin Pietersen has signed a new four-month England contract but must undergo a "reintegration" period before he returns to the team.
The 32-year-old batsman was dropped in August for sending "provocative" text messages to opposing players during the Test series against South Africa.
"It's been a horrible situation for all those involved," said Pietersen.
"I believe, all being well, I will be back in an England shirt as soon as possible."
Pietersen, who now has a central contract which could be extended until September 2013, apologised to former captain Andrew Strauss and the ECB accepts the texts were not derogatory about him.
"I'm fairly happy we're able to move forward. I'm happy we're able to draw a line under it and move on for a better result for England cricket," added Pietersen.
Pietersen was not named in the starting next month. Asked if he could still be part of the England party, he said: "I hope so. I want to play for England as soon as I can."
England's two-part tour to India ends with the fifth and final ODI on 27 January, and Pietersen's new four-month central contract covers all forms of the game.
Any decision over an extension - to make it a full-year contract - will be made by team director Andy Flower, who will also decide when the "reintegration" process is complete.
"I'd like to take this opportunity to apologise to my team-mates, all England supporters and the ECB for the situation that has arisen over the last couple of months," said Pietersen.
"Thankfully we have drawn a line under it and can move forward. Although it has been made clear in the statement, I'd like to make it clear that at no time did I share tactical information with any of the South Africans.
"I'm committed to completing the reintegration process we have agreed and representing England in all formats, hopefully until the World Cup in 2015 if my body allows.
"I want to see my son grow up seeing me play for England and hope one day he will put an England shirt on himself."
The statement said Pietersen had not retained the text messages, but gave a "binding assurance that, to the best of his recollection", they did not "convey any messages which were derogatory about the England captain, the England team director, the ECB or employees of the ECB".
ECB chairman Giles Clarke said he spent an "excellent" and "thoroughly constructive" two-and-a-half hours with Pietersen on Wednesday.
"There's lots to be done, lots to be worked out, but, in the end, we want this process to work," said Clarke.
"We wouldn't start it if we didn't want it to work immensely successfully and for England to do very well moving forward."
Former England captain Michael Vaughan told BBC Sport Pietersen would need to rebuild his relationships with team-mates.
"The issue is can Kevin Pietersen be allowed back in that dressing room?" said Vaughan.
"Now he has got a four-month trial period the only way to find out is to go into the dressing room, make a speech, get round with some of the players he has had issues with, have a beer, and try and iron it all out because you want to see the best players playing."
Pietersen averages almost 50 in Tests and, at his best, is one of the world's most prolific batsmen.
The dispute has been dragging on for more than four months after he announced his retirement from international limited-overs cricket in May before reversing that decision in August.
Discussions between the player and the ECB have been going on behind the scenes since the second Test against South Africa at Headingley, when the Surrey batsman cast doubts on his England future,a claim he later backtracked from.
Flower acknowledged Pietersen's absence has affected the team's fortunes, notably at the World Twenty20 in Sri Lanka.
England, the defending champions, were knocked out of the tournament by the hosts on Monday.
The first Test between England and India gets under way in Ahmedabad on 15 November.
England then tour New Zealand from 9 February to 21 March.