Mr Osborne was controversially announced as the head of the London Newspaper on Friday last week.
The former Chancellor, who was sacked by Theresa May when she appointed her new cabinet last year, has now penned an open letter to his voters ahead of the Tatton Conservative Association’s annual general meeting.
Mr Osbourne said: “Now I have left Downing Street I want to continue to take part in the debate about the future direction of our country.
“No longer being Chancellor gives me time to do that in other ways – yes, in the Chamber of the House of Commons; but also as the editor of a major newspaper.”
His latest appointment as editor has been met with mixed responses from his constituency.
Don Hammond, chairman of the Tatton Conservative Association, told the Telegraph: "I know a number of constituents do have concerns, we have an AGM on Friday.
"He is a very talented MP and a good guy. There are mixed views about his taking the job."
Christopher Gray, a town councillor in Knutsford, Cheshire, said: "I have mixed views. I have done two jobs in the past. There is a time element. He has been an extremely good MP for Tatton.
George Osborne was sacked for his position as Chancellor last year
I know a number of constituents do have concerns… there are mixed views about his taking the job
Don Hammond, chairman of the Tatton Conservative Asso
“I’m not quite sure he can continue in the same way he has done. There is a saying that he who pays the piper calls the tune."
While Angus Reilly, chairman of Tatton constituency Labour Party, has called for Mr Osborne to resign as the Tatton MP.
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He said: “This has only proven what the people of Tatton have known all along.
“George Osborne’s focus is not on the people of Tatton. He should not continue as a Member of Parliament.”
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But the Tatton MP has defended his recent appointment.
Mr Osborne said: “There is a long tradition of politics and journalism mixing.”
“One of the greatest newspaper editors ever, CP Scott, combined editing the Manchester Guardian with being an MP.
“In our age, politicians from Iain Macleod and Richard Crossman to, of course, Boris Johnson have combined the role of editor and Member of Parliament.”
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There have been calls for a probe into whether Mr Osborne broke rules for former ministers by failing to clear the appointment with the Advisory Committee on Business Appointments (Acoba) before it was announced.
Lord Paul Bew told The Sunday Times: "We have not ruled out MPs having second jobs, quite deliberately, up until now, but we now have to look again at our rules.
"We are going to discuss whether our rules on second jobs need to be changed in light of this.
"We had something that up to a degree worked. It now seems to be getting into rockier waters."
The Tatton MP’s other jobs include £650,000 a year for advising the investment managers Blackrock, almost £800,000 for being a speaker on the Washington Speakers bureau, and £120,000 for being the Kissinger Fellow for the McCain Institute.