The Times reports that Arsenal have agreed to pay an initial £70m plus £10m in add-ons for Guimaraes, who is poised to sign a five-year contract once the move is finalised.
The Brazilian has been a priority target for Mikel Arteta all summer as Arsenal look to strengthen a squad that won the Premier League title last season, and is understood to have been receptive to the move given Newcastle's struggles to match his ambitions.
The move comes after Guimaraes delayed meeting up with Newcastle's squad, who flew out to La Manga on Friday for pre-season training, having been given three weeks off following Brazil's World Cup campaign, which ended in a last-16 defeat to Norway.
Newcastle United had remained hopeful of keeping their captain throughout the saga, and it is understood the club grew increasingly frustrated with a perceived lack of direct communication from Arsenal until talks intensified in recent days.
Guimaraes's departure adds to a difficult summer on Tyneside that has already seen winger Anthony Gordon leave for Barcelona, midfielder Sandro Tonali join Tottenham Hotspur, and head coach Eddie Howe step down after nearly five years in charge.
Howe, who brought Guimaraes to England from Lyon in January 2022, received an emotional tribute from the midfielder after his departure was confirmed, with Newcastle since moving to appoint Matthias Jaissle as his replacement.
Guimaraes's exit would represent Arsenal's most significant midfield addition of the summer, arriving alongside interest in Real Madrid's Vinicius Jr as Arteta looks to add further quality to a squad already boosted by the permanent signing of Piero Hincapie, plus the arrivals of goalkeeper Illan Meslier and winger Christos Tzolis. The move is also set to trigger a domino effect in Arsenal's own squad, with Christian Norgaard's £7m exit to Everton, reported separately on Saturday, expected to create the space in midfield needed to accommodate Guimaraes.