The controversial former MP, who was booted out of the Labour Party in 2003, says he will stand as an independent in West Bromwich East on a pro-Brexit platform, while extolling "the traditional values of the labour movement".
Labour deputy leader Mr Watson has held the seat since 2001 and has a majority of 7,713.
A crowdfunding campaign set up by Mr Galloway had reached nearly £5,000 of its £25,000 goal by midday today.
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In a statement he said: "I seek to replace Tom Watson MP. I am the Prospective Parliamentary Candidate for West Bromwich East constituency.
"I will stand as an Independent candidate supporting Brexit and the traditional values of the labour movement; the values of Tony Benn, Michael Foot, Barbara Castle, Peter Shore etc.
"My work in West Bromwich East has already begun and I intend to crowdfund my campaign.
"I hope you can help, either with a one-off donation or regular contributions. Tom Watson has the biggest of backers and I do not.
"But many make much; I stand for the many and I hope many will support me. All unspent monies will be distributed to local food banks."
Mr Watson said:
“Galloway has caused more reputational damage to Jeremy Corbyn’s Labour Party than any single other politician.
"And if he is serious about standing in our area, he’ll have to explain to every resident why he fawned so pathetically to Saddam Hussein. We’re patriots here.”
Four years out of parliament
Mr Galloway was last an MP for the Respect Party he set up, losing his Bradford West seat in 2015.
A long time critic of Israel, he once declared Bradford "an Israel-free zone" and was last month sacked from his TalkRadio show after he was accused of sharing anti-Semitic views on social media.
The former MP tweeted that Liverpool’s victory over Tottenham in the Champions League final meant there would be “no Israel flags on the cup”.
The tweet was condemned by Mr Watson, who welcomed his dismissal from the station and accused him of "hatred and bigotry".
Mr Galloway has become a major critic of Mr Watson in recent years, saying that he was "embarrassed" that he used to like him and describing him as "a byword for disloyalty and for treachery".
The pair's views on Brexit contrast markedly, with Mr Galloway in favour of leaving the EU and Mr Watson calling for Labour to campaign for Remain in another referendum.
At the 2017 election, Mr Watson won 58 per cent of the vote (22,664), with Conservative candidate Emma Crane coming second with 38.2 per cent (14,951).