The 28-year-old has put pen to paper on a four-year deal with a further one-year option.
On the move to Arsenal, Guimaraes, who will wear the no. 39 shirt with the Gunners, said: "I feel amazing. I'm glad for the opportunity. Since the first time I spoke to [Andrea] Berta and Mikel [Arteta], I was excited. I just felt inside of me that I need a new challenge in my life and I think to be an Arsenal player is going to be an exciting challenge in my life.
"I'm so excited to join you. I will give you my best, I promise. I'm your warrior, I'll never give up. Hopefully we can create many, many good memories together."
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'Bruno will allow Arsenal to develop playing style'
Arsenal sporting director Andrea Berta added: "We are delighted to welcome Bruno Guimaraes to our club. Bruno is a player with a great mentality and great quality, who will bring strong leadership to our squad.
"With Bruno joining us, we are further strengthening the heart of our team. As we have all seen, Bruno can play as a defensive midfielder and as a box-to-box player. He combines quality with quantity, and has provided goals and assists for his team every year.
"Bruno will allow Mikel to further develop our playing style and will also increase our internal competitiveness, which is essential for maintaining the standards required when we are aiming to win major trophies."
Newcastle had been keen to ensure the Brazil international, who had two years left on his contract plus a club-held option for a third, stayed at St James' Park, but his departure means they have now sold more than £240m worth of talent this summer.
Anthony Gordon joined Barcelona in a £69.3m deal and Spurs signed Sandro Tonali for £100m, while head coach Eddie Howe also left in what has been a turbulent few months at the club.
A Newcastle statement said: "The agreed fee represents one of the top-10 highest transfer fees ever received for a player aged 28 or over, and a record fee for a player of his age and position combined."
Guimaraes told Newcastle bosses earlier this summer that he wanted to join Arsenal if a suitable offer arrived. Their opening bid was rejected before the deal was agreed.
He joined the Magpies in 2022 from Lyon for £40m and made 195 appearances for the club, scoring 31 goals and winning the Carabao Cup.
'One of the toughest decisions of my life'
On his Newcastle departure, Guimaraes said: "This is one of the toughest decisions of my life. When I arrived, the club was in a challenging position and I am incredibly proud of what we achieved together.
"I fell in love with this place. I really mean that. From my first day, the supporters, my team-mates, Eddie (Howe) and the staff, and everyone connected with the club made me and my family feel at home.
"I thank PIF, our chairman Yasir Al-Rumayyan and Jamie Reuben for everything they have done for me and for this football club. I also want to say thank you to David (Hopkinson) and Ross (Wilson) for the huge respect to me throughout this process. They did everything they could to keep me at Newcastle, and I am very grateful for our time together.
"This move is very tough because Newcastle means so much to me, but I wanted to experience something new in my life. I feel ready for a new challenge for myself and my family. I had a very positive conversation with Matthias Jaissle, and I leave knowing the club is in very good hands.
"To the supporters, thank you will never be enough, but I say it with all my heart. I will always be proud to have been part of this club's journey. Thank you for everything."
'A statement signing for Arsenal'
Sky Sports' Oliver Yew:
Guimaraes is one of the best midfielders in the Premier League, if not the world, and from a position of strength, Arsenal have taken him from Newcastle.
Midfield is already an area of the pitch where Arsenal are strong but Guimaraes' arrival is certainly an upgrade on Christian Norgaard, who has joined Everton. Myles Lewis-Skelly was playing incredibly well at the end of last season and started the Champions League final. Martin Zubimendi and Mikel Merino are World Cup winners and after some rest will be ready to go. There is Martin Odegaard and Eberechi Eze for the No 10 position alongside the two potential starters in Declan Rice and Guimaraes.
The Brazilian gives Arteta even more options and it also allows for the possibility for Rice to get a breather in certain games after his exploits last season.
It is a world-class midfield and if Arsenal were not favourites for the title already, they are now.
Question marks were being raised over the fee Newcastle wanted for a player who will be 29 in November but the deal has been done nowhere near the reported £100m fee that was wanted. At the start of the transfer window, you would have probably said this is a fair fee, but with the last few weeks we have had in the window, with big money spent on midfielders Elliot Anderson and Morgan Rogers, anything under £100m looks good value.
Guimaraes is a little older but this is Arsenal's strategy, they want to win now. They have signed some younger players but last summer's deal to sign Viktor Gyokeres was to win now. He will not need any time to settle in. He is one of the most consistent Premier League midfielders.
Arsenal will not necessarily make money on him in the future but his arrival should get them closer to winning a first Champions League and he may help them retain the Premier League title.
If they can add a left winger and some star quality in that position, which looks like the last piece of the puzzle, it could be bad news for their title rivals.
'Newcastle were desperate to keep Guimaraes'
Sky Sports News reporter Keith Downie:
Newcastle were desperate to keep Guimaraes and if he had said he wanted to stay, Newcastle would have refused any offer from Arsenal or any other club.
Attempts to persuade Guimaraes otherwise were made and positive conversations were held, but he was insistent he wanted to leave because he felt this was his last big opportunity to win titles.
The deal could only go ahead if two things happened: Guimaraes said he wanted to leave (which he has respectfully) and Newcastle sold on their terms, similar to Sandro Tonali and Anthony Gordon.
Newcastle insisted it was their valuation or no deal. They would only sell Guimaraes at a fee that would become one of the highest paid for a player aged 28 or over.
In addition, a deal would only be sanctioned if the situation was handled properly - for example, Guimaraes attending Newcastle's training camp in Spain, which he reported to on Monday.
Newcastle feel Guimaraes has complied with their demands immaculately. They did not want a repeat of the Alexander Isak situation, where he refused to train before joining Liverpool last summer.
Agents were in between the clubs from the outset but Newcastle refused all pushes, which had began with mentions of a deal worth £40-£45m in June.
Newcastle were left frustrated because they felt Arsenal elongated the transfer by refusing to contact them for weeks.
Newcastle insist there have been no fall outs and good relations remain between player and club.
