With Jeremy Corbyn's far Left leadership leaving Labour in chaos and unable to form an effective Opposition, Mr Osborne has filled the gap.
In his letter, he said Osborne was required to refer any new job he meant to take within two years of leaving office to the Advisory Committee on Business Appointments (Acoba) before accepting it.
The MP for Tatton now has a total of six highly paid jobs including his constituency work, as editor of the Evening Standard, chair of the Northern Powerhouse partnership, an adviser to BlackRock, academic work as a Kissinger fellow in the U.S., and an after-dinner speaking contract.
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 Mr Osborne's new role.
Parliament's Committee on Standards is looking at reviewing its rules to outlaw MPs taking on jobs which affect their constituency duties. "It now seems to be getting into rockier waters".
"We are going to discuss whether rules on second jobs need to be changed in light of this".
But Mr Osborne's elevation to the job, set to be vacated by current editor Sarah Sands in May, was welcomed by former prime minister Mr Blair.
SNP MP Tommy Sheppard, who sits on the Committee on Standards, added to 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".
Karanka walked away to save Middlesbrough says owner
MIDDLESBROUGH chairman has no plans to approach Nigel Pearson or Steve McClaren to replace Aitor Karanka. Gibson told the Times newspaper: "I've had a lot of discussions with Aitor since the weekend.
He said: "You can not edit the Evening Standard and represent your constituents in any meaningful sense".
Evgeny Lebedev, owner of the newspaper, tweeted: "I am proud to have an editor of such substance, who reinforces the Standard's standing and influence in London and whose political viewpoint - socially liberal and economically pragmatic - closely matches that of many of our readers". "Why not? He is a highly capable guy and it should make politics more interesting", he told BBC1's The Andrew Marr Show.
'How many votes would you miss in the Commons, for example?
She told the same programme: "I have to say I thought "well, he's a better man than me" because I spent ten years as a journalist, I've now spent six years as a politician and I'm not sure you can combine them both".
"I wouldn't be letting someone else do it and I just don't think it works".
Labour MP Jess Phillips wrote: "Everybody in my office has a "WTF" expression on their face about the George Osborne news". "Well, George Osborne is a very clever man - I am sure he could do anything he puts his mind to" she said.
Among Evening Standard journalists there was a degree of scepticism over Lebedev's statement implying that Osborne had applied for the job, rather than it being the "strange and cosy" deal between dinner party pals that most of the staff suspect. "And will stand up for the interests of London and Londoners".