It has occurred outside of the usual transfer window periods, with the January cut-off deadline having passed on January 31.
As well as that, the nature of the deal has upset Leganes, who have complained to the Spanish football authorities that it leaves them at an unfair disadvantage.
So, why are Barcelona allowed to sign the Denmark striker at all? Goal has the details.
Why can Barcelona sign Braithwaite outside the transfer window?
Barcelona availed themselves of an exemption by La Liga and the Spanish football association (RFEF) to sign Braithwaite outside of the regular transfer window following a season-ending injury to Ousmane Dembele.
In cases where players have been ruled out of action for five months or longer, it is deemed that an emergency transfer or signing is a reasonable request and administrators can facilitate it.
The Catalan club were given the green light to sign Braithwaite within RFEF regulations, which stipulate that a player can be brought in if they are a free agent or if they are contracted to another club in La Liga.
Since they were replacing Dembele, the replacement signing had to be like-for-like - that is, another forward - and a time limit of 15 days was put in place.
Why is the Braithwaite to Barcelona transfer considered unfair?
The transfer of Braithwaite to Barcelona has placed Leganes in a difficult position because it has seen them lose a key player while also being unable to sign a replacement.
While Barcelona are pushing for La Liga glory, Leganes find themselves at the other end of the table fighting against relegation and Braithwaite was their top goalscorer.
His departure for Camp Nou serves to compound the difficulties faced by Los Pepineros, who had already been forced to contend with losing striker Youssef En-Neysri to Sevilla in January.
Leganes general director Martin Ortega told reporters: “We consider that there is a regulation that is unfair, from which Barcelona has benefited. The one who is damaged by this is Leganes."
The club are attempting to minimise their difficulty by appealing to the Spanish football authorities for a chance to sign a replacement for Braithwaite.
How much did Barcelona pay for Martin Braithwaite?
Barcelona paid a fee of €18 million (£15m/$19m) to Leganes in order to bring Braithwaite to Catalunya.
Leganes were forced to accept the bid as it met the Denmark international's release clause.
The 28-year-old has agreed a four-and-a-half-year deal with the Blaugrana and his new release clause has been set at €300m (£252m/$324m), which is quite a jump from his previous buy-out clause.
Who is Martin Braithwaite?
Braithwaite made a permanent move to Leganes in the summer of 2019, scoring a total of 10 goals in 43 La Liga appearances for the club before transferring to Barcelona in February 2020.
He has been a regular member of the Denmark international squad since making his debut in 2013 and played for his country at the 2018 World Cup.
He will become the fifth Danish player to line out for Barcelona, following in the footsteps of Allan Simonsen, Michael Laudrup, Thomas Christiansen and Ronnie Ekelund.