Gordon will undergo his medical with the Catalan giants on Thursday before putting pen to paper on a long-term contract at the Camp Nou.
Barcelona made their interest in Gordon known this week and after initial talks negotiations progressed quickly.
Bayern Munich wanted Gordon this summer but didn't agree with Newcastle's valuation of the England international, which allowed Barcelona to strike.
Liverpool were also said to be closely monitoring the situation but Gordon is now set to be confirmed as a Barcelona player before the end of the week.
It's understood the up-front fee will be £70m - plus add-ons. Personal terms won't be an issue.
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Gordon has been a key figure in Newcastle’s return to prominence in recent seasons, and his attacking partnership with Alexander Isak, who moved to Liverpool for £130million last summer, and Jacob Murphy has been a key feature.
He did not play in the final because of suspension, but his form was one of the driving forces in the run which helped the club end its 70-year wait for a major domestic trophy in the 2024-25 Carabao Cup final and also qualify for this season’s Champions League.
However, amid repeated speculation that he could leave Tyneside, Gordon’s influence has waned somewhat this season despite a return of 17 goals, 10 of them – including one against Barcelona – in the Champions League.
As the rumour machine went into full swing with the end of the campaign approaching, head coach Eddie Howe decided to leave the player out of his team on his return from injury, citing the need to focus on the future, perhaps an indication of what is to come.
Gordon almost joined Liverpool two summers ago when Newcastle were forced into quickfire sales to ensure they didn't fall foul of PSR restrictions, but the forward's move to Anfield fell through.
Barcelona were in the market for a left sided attacker this summer, and while uncertainty continues to surround Marcus Rashford's future after his loan spell with the club, the La Liga title winners have acted quickly to secure the signing of Gordon.
Everton will be in line to receive a percentage of the profit having included a sell-on clause when they sold Gordon to Newcastle in 2023.
Gordon's last Newcastle appearance in the Premier League defeat to Crystal Palace in early April and then missed the following two games with injury. He returned to the squad for the win over Brighton but was an unused substitute for the last four games.
Asked if he was not using Gordon because he had one eye on the future, Howe said: "When you get to this stage of the season, part of what we will be doing we'll be looking to next year, naturally, so yes.
"Anthony's just come back from injury. I think the team has played well in his absence and with a partial view to the future, yes."
Newcastle chief executive David Hopkinson admitted a couple of months ago that trading will be key for the Magpies this summer, but said Newcastle would only sell on their terms.
Gordon will leave Newcastle having made 111 Premier League appearances and scoring 24 goals.
Strengthening the attack is a priority for Newcastle this summer. As well as looking to bolster on the flanks, the Magpies are in the market for a centre-forward.
It's set to be a summer of change on Tyneside, with Gordon joining Kieran Trippier through the exit door.