The former chancellor will take up his role at the newspaper in May and said he intends to carry on representing his Cheshire constituency of Tatton - 190 miles from the capital – in Parliament.
But the chairman of the Committee of Standards in Public Life told the Sunday Times that the body would discuss whether the rules on second jobs need to be changed in light Osborne’s new role.
Lord Bew said: “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.”
Lord Bew told the paper the editor role did not fit the current policy on second jobs, but stressed that the issue was “not personal” to Osborne.
However, he said his case raised the “issue of how much time MPs have to devote to their parliamentary work”.
SNP MP Tommy Sheppard, who sits on the Committee on Standards, told the Sunday Telegraph there was “broad agreement” that an additional job “must be something that demonstrably doesn’t prevent you doing your first job as an MP”.
He said: “You cannot edit the Evening Standard and represent your constituents in any meaningful sense. How many votes would you miss in the Commons, for example? It beggars belief.”
Osborne’s appointment has sparked calls for an inquiry into whether he broke rules for former ministers by failing to clear the appointment with the Advisory Committee on Business Appointments, which vets new jobs taken by senior public figures.
He has previously faced controversy for accepting a post as an adviser to the US asset management fund BlackRock for £162,500 a quarter for 12 days working as an “adviser on the global economy”, while racking up more than £780,000 in speaking fees since leaving office.
The MP also gets £120,000 in relation to fellowship at the Washington-based McCain Institute think tank while continuing as the unpaid chairman of the Northern Powerhouse Partnership.