Mr Watson, MP for West Bromwich East, reacted with surprise after the sudden announcement that George Osborne is to become the new editor of London's Evening Standard newspaper - and to continue as an MP.
The move has stunned the newspaper industry. Mr Osborne, who was sacked from the Cabinet by Prime Minister Theresa May, has little experience as a journalist, although he once applied for a trainee position on The Times and was turned down.
He will take up his role in May, editing the newspaper four days a week, but will remain as Conservative MP for Tatton, in Cheshire.
Many people at Westminster are wondering how he can hold down both jobs and they include Mr Watson, who said on Twitter: "The long hours and early starts that editing a paper like the Evening Standard requires are incompatible with the demands placed on MPs."
He added: "I assume the former Chancellor will give up his seat and trigger a by-election, possibly to coincide with the elections being held in May."
The long hours and early starts that editing a paper like the Evening Standard requires are incompatible with the demands placed on MPs.— Tom Watson (@tom_watson) March 17, 2017
I assume the former Chancellor will give up his seat and trigger a by-election, possibly to coincide with the elections being held in May.— Tom Watson (@tom_watson) March 17, 2017
The Evening Standard is distributed free in London and the surrounding area. It is one of the few "evening" newspapers left in the UK, though like other evening papers it is actually available in the afternoon.
The paper is particularly influential because it is seen by politicians and journalists for national media organisations during the day. That means it can influence the way broadcasters treat stories in evening TV and radio bulletins, as well as the next day's papers.
Like other newspapers, the Standard also now has an active website and presence on social media such as Twitter.
Mr Osborne will add the editorship of the Evening Standard to a growing list of jobs since leaving Government.
Since February, he has been earning £650,000 a year for one day a week's work at Blackrock Investment Institute.
He has also earned almost £800,000 from speaking engagements.
As an MP he has a basic annual salary of £74,962.
Mr Osborne said: "Growing up as a Londoner, I've always known that the Evening Standard is an institution that plays a huge part in the life of the city and its people.
"Now it is a great honour that I can play a part as leader of the editorial team making the Evening Standard the definitive voice of the world's most exciting city.
"I am proud to be a Conservative MP, but as editor and leader of a team of dedicated and independent journalists, our only interest will be to give a voice to all Londoners."
A spokesman for Labour leader Jeremy Corbyn said Mr Osborne should stand down and allow a new MP to be elected in his Tatton seat.
The spokesman said: "We are looking forward to an early by-election so the people of Tatton are properly served in parliament.”
Shocked reaction to George Osborne's appointment
Media commentators, journalists and politicians have reacted with shock and bafflement upon learning that George Osborne has been appointed the editor of the London Evening Standard.
Leading the reaction was former leader of the Labour party Ed Miliband, who mocked the news, writing on Twitter: "Breaking: I will shortly be announced as editor of Heat magazine...."
Many took to social media to comment on Mr Osborne's qualifications, while others questioned his ability to both edit the newspaper and continue his work as an MP simultaneously.
Labour leader Jeremy Corbyn shared his view on the announcement, saying that it is "taking multitasking to an extreme level" and calling it a "joke".
Liberal Democrat leader Tim Farron had a similar sentiment to Mr Miliband, writing: "I guess I should apply to edit Viz then?"
Political broadcaster and former editor of The Sunday Times Andrew Neil said: "My threshold for being shocked just rose a little more: George Osborne new Editor of Evening Standard. And it's not even fake news."
Neil added that "we can rule out it ever backing Labour or Lib Dems", due to Mr Osborne remaining a Tory MP.
He wrote: "When made Editor of The Sunday Times I was criticised because I hadn't been an editor. Mr Osborne hasn't even been a journalist."
ITV News' political editor Robert Peston wrote: "I find it very hard to believe Tory Party won't force @George-Osborne to make a choice between editing @EveningStandard & being an MP."
Nick Robinson, presenter of BBC Radio 4's Today programme, wrote: "Wow. For many years @George-Osborne has joked with me & fellow hacks that he's always really wanted to do our jobs."
Sathnam Sanghera, writer and columnist for The Times, wrote: "Excuse to share one thing I have in common with George Osborne: we were both rejected for Times graduate training scheme. But we're fine now ... I hope his transcribing skills are on point."
Labour politician Jess Phillips wrote: "Everyone in my office has a "WTF" expression on their face about the George Osborne news.
"Flooded with offers of writing and media to comment on Osborne, the answer is No, I can't do anything til 8pm as I have a job to do as an MP."
Labour MP Jo Stevens said she would be "pretty pissed off" if she were a member of Mr Osborne's constituency of Tatton, adding the hashtag "£2jobsOsborne".
Ann Gripper, the executive editor for the Mirror Online, wrote: "If George Osborne thinks he can remain an MP as well as being editor of the Evening Standard then he has no idea what either job involves."
"Congratulations to @George-Osborne who 20 years after applying to become a journalist has finally made it," political journalist Jane Merrick wrote.
She added: "Am hearing that David Cameron's about to be unveiled as the new editor of Vogue..."
Amid the overall reaction of shock, London mayor Sadiq Khan sent well-wishes to Mr Osborne, writing: "Congratulations to @George-Osborne - the new editor of the @EveningStandard. Covering the world's greatest city £LondonIsOpen."
On the lighter side, there were plenty of jokes made comparing Mr Osborne's new position to that of newly announced presenter of The Great British Bake Off Noel Fielding.
Writer and editor at Buzzfeed Matthew Champion quipped: "Thursday: Noel Fielding named host of GBBO. Fri: George Osborne new editor of Evening Standard. Sat: Sonic the Hedgehog becomes Labour leader."
Guardian columnist Tim Dowling wrote: "George Osborne editing the Standard, Noel Fielding on Bake Off. Now I regret not applying to be the Astronomer Royal."