The 21-year-old helped the Porto Alegre club to the final of the Copa Libertadores and put in an impressive performance in the second leg as they ran out 3-1 aggregate winners over Lanus of Argentina.
Barca were subsequently linked with Arthur, and reports from Spain and Brazil claimed that the two clubs had been in discussions over a potential transfer earlier in March.
The Catalan giants have now reached an agreement to secure first option on the player, who will cost £26.6m plus £8m in add-ons should the Blaugrana choose to activate the deal in July.
"FC Barcelona and the Brazilian club Gremio de Porto Alegre have reached an agreement on a purchase option for the player Arthur Henrique Ramos de Oliveira Melo, whereas FC Barcelona may exercise this right on the player's federative rights during July of 2018," Barca said in a statement on Sunday.
"In the event that the club finally exercises the option signed, the price of the transfer is set at €30m plus €9m in variable amounts."