The Red Devils made the announcement on Friday evening, with the transfer now subject to the agreement of personal terms, UK visa requirements, and a medical.
It is understood that the deal could be worth as much as £70 million.
Casemiro has enjoyed a hugely successful spell during his time in the Spanish capital, winning five Champions League title and three La Liga titles among other honours.
Unsurprisingly, news of the high-profile transfer has courted widespread reaction from across the footballing world.
And while there has been plenty of positivity, there have been some more sobering opinions expressed as well, including that of renowned Spanish journalist Guillem Balague.
The reporter has praised the 30-year-old’s leadership qualities, but has questioned how he will fit into Erik ten Hag’s preferred tactical approach.
Here’s everything you need to know...
What has Balague said about Casemiro?
Writing in a column for BBC Sport, Balague warned that United risk exacerbating the weaknesses in the Brazilian midfielder’s game if they continue to adhere to Ten Hag’s insistence on a high-pressing style of play.
He said: “If Erik ten Hag is to remain faithful to his high-pressure philosophy, with a high defensive line, then Casemiro’s lack of pace will be exposed.
“He lacks the ability to control the spaces behind him, primarily because he is quite slow on the turn. This could prove expensive against teams such as Arsenal and Manchester City, who play a lot of inside passes and find pockets of space.
“Madrid’s compact set-up disguised that weakness in Casemiro’s game. With less quality around him in the Brazilian national side, he was less influential. That could be a problem with United when faced with teams that pressure high if he is expected to drive with the ball.”
The respected journalist did, however, also highlight a number of the positive attributes that the 30-year-old should bring to United’s midfield.
He added: “[Carlo] Ancelotti has asked him to go forward more often, occasionally taking on an offensive midfield role, and he scored seven times last season - equalling his career best for a campaign. He will add goals from midfield for United - he has a powerful shot and is a great header of the ball.
“He is a leader and a winner who reads the game exceptionally well - and English referees will show more tolerance to his robust approach than he is used to - but it remains difficult seeing how he will fully function in a Ten Hag system.
“Despite being the best defensive midfielder in a system that lives on the edge of its own box and attacks as a unit at a slower pace, he will now find himself competing in a league where games are played at a much quicker tempo, and where most teams are faster and stronger than he is used to.
“For Ten Hag, it will be a case of finding the right balance to make sure the new arrival fits in as best as possible. To do that, he will have to adapt.”
What else has been said about Casemiro?
Former United defender Rio Ferdinand has been quick to hail the deal, but like Balague, also admitted that there are concerns about Casemiro’s arrival.
Speaking on his YouTube channel, the former England international said: “Wow, listen man... That’s the type of player Man United need, the type of character Man United need more than anything. He’s the type of person, individual.”
Ferdinand went on to address the £70 million fee attached to the deal, adding: “Is he overpriced? Yes.”
The pundit then went on to deliver a detailed view on what he thinks United fans can expect from their newest recruit.
He said: “The positives I’ll start with... First and foremost, the guy’s a real winner, he knows how to win, he’s been integral in everything positive about Real Madrid in recent years.
“[He has been] one of the main guys alongside the likes of Luka Modric, Toni Kroos, Karim Benzema.
“When the big games come along, this guy performs. He knows what he’s doing, he’s there.
“There’s no thrills with him. He isn’t a stepover merchant, he isn’t a skills man, he isn’t someone who wants to get the fans off their seats with a bit of skill. He’s there to do a job that means that the team are better off, they run more efficiently, they’re going to have a chance of winning because he’s in the team.
“He’s first and foremost a team football player, which I love about him. If there’s a battle, he’s a man you want on your side.”
Ferdinand continued: “Are there negatives? Yes there are.
“Obviously the age, 30 years old, I wouldn’t say that’s a massive negative, but if you’re talking from a business standpoint from the club’s perspective, there’s going to be zero re-sale value.
“You’re probably looking at somewhere near £100million with the wages. If you get change out of that you’ll be lucky.
“To come from Spain for Casemiro into a team that is absolutely bereft of any confidence, is absolutely struggling in all areas, tactically especially, physically, mentally... I think it’s going to be a huge ask for a 30-year-old to come in, recharge, reboot and go again.
“He’s been doing that and been successful in a team that’s very well-drilled with consistent players there, consistent method and philosophy, a way of playing.
“[But] he’s coming to somewhere now where everything is brand new in terms of the coaching, behind the scenes it’s brand new. People starting to try and decipher what’s good, what’s bad. There’s a lot of uncertainty behind the scenes and confidence is very low.
“In the Premier League, the spaces around you are bigger. That’s where he may have some difficulty, but if the team is tight around him he’ll be fine. You need people that know how to get the job done.”