Guimaraes offered an emotional goodbye to his team-mates and staff before departing the club’s pre-season camp in Spain.
His exit makes him the fourth major departure in under a year.
Earlier in the window, Sandro Tonali and Anthony Gordon moved to Tottenham Hotspur and Barcelona respectively, while Alexander Isak joined Liverpool last summer.
Losing Guimaraes is especially painful given his talismanic role, but Newcastle chief executive David Hopkinson said Arsenal initially pushed for a lower fee after smaller figures were floated for a player who turns 29 in November.
He also acknowledged that Newcastle would have preferred “an even higher number” for a player of such influence.
Hopkinson noted that both sides are experienced negotiators and that this is simply how deals get done.
He added that the price meets the club’s expectations and, from a marketing standpoint, represents a record for a player of that position and age.
He believes it’s a good outcome for Newcastle United, while pointing out that Arsenal are acquiring a special player and person, and that financially it works for both clubs.
Newcastle are already moving in the market to find a replacement.
Although four of Newcastle’s five summer signings have been 20 or younger, the club now want a more experienced midfielder and aim to make a couple of further additions before the window closes on 1 September.
However, Wilson cautioned against rushing into a deal merely to tick a box.