Mr Gove was moved from his education post to Chief Whip in yesterday's reshuffle, with the Prime Minister claiming he wanted "one of my big hitters, one of my real stars" in the position ahead of next year's General Election.
The Chief Whip also played down suggestions he was demoted, saying: "Demotion, emotion, promotion, locomotion, I don't know how you would describe this move - though move it is."
He also claimed Mr Cameron gave him the option of staying as the Education Secretary.
Michael Gove has paid tribute to his successor as Education Secretary, describing Nicky Morgan as "one of the most intelligent" people he has worked with in government.
The Education Secretary also told ITV News Political Editor Tom Bradby his new job as Chief Whip meant he could play a role in ensuring a future Conservative government would be "a genuinely reforming government and also a genuinely socially progressive government".
He also indicated that he had been involved in other ministerial reshuffle moves, saying he had "played a role over the course of the last week with the Prime Minister and with the Chancellor" in making sure "the right people" were in place for the Conservatives.
David Cameron has hailed outgoing Education Secretary Michael Gove as "one of my big hitters, one of my real stars" and said he was pleased to have moved him into one of the most important jobs in government.