Arsenal's opening offer for the 28-year-old Brazil midfielder was rejected earlier this week, but the London club returned with an improved bid and have now reached an agreement with Newcastle, according to Sky Sports.
Reuters has contacted both clubs seeking confirmation of the deal.
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Guimaraes had previously told Newcastle that he wanted to join Arsenal if a suitable offer arrived, reports suggested. Newcastle were keen to retain their captain, who has two years remaining on his contract at St James' Park as well as an option for a further year.
The midfielder joined Newcastle from French side Olympique Lyonnais in January 2022 and had become one of the club's most influential players.
He has made 195 appearances in all competitions, scoring 31 goals, and helped Newcastle end a long wait for domestic silverware by captaining them to League Cup success in 2025.
Guimaraes would add further quality and experience to Mikel Arteta's midfield as Arsenal look to defend the Premier League title and challenge in Europe.
The Brazilian international featured for his country at the 2026 World Cup and has been a regular presence in the national team in recent years.
The move will come as another blow for Newcastle after the departures of key players Anthony Gordon and Sandro Tonali, as well as manager Eddie Howe.