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Your Site News understands the fee is £69.3m (€80m) inclusive of add-ons.
Gordon, who finished this season as Newcastle's top goalscorer with 17 goals, signed a long-term contract extension at St James' Park in October 2024 and had four years remaining on that deal.
Your Site News' Keith Downie:
"What's interesting is the two clubs who were fighting for his signature are from the continent - Barcelona and Bayern Munich - and I think a lot of that would be down to what he's done in the Champions League this season.
"Only Kylian Mbappe and Harry Kane scored more goals than Gordon's 10. It's a brilliant return. In that competition, his numbers have been sensational. His numbers haven't been quite as good in the Premier League.
"Yes, he scored six, taking his total to 17 which, on paper, looks good. But clearly his best form this season has been reserved for the Champions League.
"He can play a number of positions, too. Ordinarily, he's played off the left-hand side in a 4-3-3, but he's also been used a lot through the middle, to devastating effect at times.
"Barcelona have got an abundance of riches, with the likes of Lamine Yamal and Raphinha. Robert Lewandowski is leaving, so perhaps that provides an opening for him through the middle. That ability to play in a number of positions is the thing that has attracted Barcelona.
"He's got blistering pace, he scores all sorts of goals and he's improved greatly as a Newcastle player since arriving from Everton. He's 25, he's an England international and I can see him fitting into the lifestyle over there, the style of football.
"Newcastle fans will be disappointed they are losing one of their star players, however I think it's easier to take losing him to Barcelona than it would have been if they were to have lost him to Arsenal, who were interested, and Liverpool, who almost signed him two years ago."
