The midfielder, who has scored three goals in 160 appearances for Arsenal since his senior debut in 2008, has struggled to get games this campaign and featured in just seven league matches, coming on as a substitute in six of them.
The board asked Mascherano to stay at the club until Yerry Mina arrived.
It is also reported that the termination clause of the Colombian defender's contract will be €100 million.
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Barca say they have signed a "quick, ball-playing defender" who can also use his "aerial prowess to impose himself and score goals".
Barcelona had an agreement with Palmeiras to bring Mina in the middle of this year for about 9 million euros, but agreed to pay extra and advance the deal because of Umtiti's hamstring injury.
Mina is known for his speed and daring.
Mina joined Palmeiras from Sante Fe previous year, and he proved an instant success. He won the Brazilian league title in 2016 and Copa Sudamericana with his former club Santa Fe. Mina's transfer included a transaction fee of $14.2 million.
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Mina will be the first Colombian to play for Barcelona and Faustino Asprilla tweeted a graphic of the signing.
Mina is set to play in his first World Cup in Russian Federation this year.
The Madristas are 16 points below league leaders and occupy the fourth position in the La Liga.
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