Guimaraes bid a tearful farewell to his team-mates and to staff before leaving the club’s pre-season training camp in Spain.
He will become the fourth key player to move on in less than a year.
Sandro Tonali and Anthony Gordon joined Tottenham Hotspur and Barcelona respectively earlier in the window, while Alexander Isak went to Liverpool last summer.
Losing Guimaraes is a particular blow, given his status as the club’s talisman, but Newcastle chief executive David Hopkinson suggested Arsenal had hoped to pay a smaller fee after lower sums were initially floated for a player who turns 29 in November.
However, Hopkinson recognised that Newcastle, conversely, would have liked “an even higher number” for such an influential figure.
“You’re dealing with very sophisticated actors on each side,” he said. “That’s what negotiation looks like.
“It’s a fee that satisfies us. If you want to put a merchandising spin on it, it’s the highest fee for a player in that position at that age, and all those things come into play.
“Is it a good deal for Newcastle United? I believe it is, but Arsenal are getting a very special player and person. It’s worked from a financial perspective for both sides.”
Newcastle are active in the market to bring in a replacement.
Four of Newcastle’s five signings this summer have been aged 20 and under, but the club are looking to sign a midfielder with a little more experience, and make a couple of further additions beyond that before the window shuts on 1 September.
However, Wilson warned they don’t want to make “any mistakes by jumping to do something that we don’t really want to do to tick a box”.
