Barcelona have agreed a €40 million (£35m) deal with Gremio to sign Arthur, according to reports in Brazil.
The La Liga leaders have been in talks with Gremio for several months, while the midfielder was pictured wearing a Barcelona shirt after holding secret talks in December.
The 21-year-old is widely regarded as one of the brightest prospects in Brazilian football and has been also been linked with Manchester United and Chelsea.
But according to UOL Esporte, Barcelona and Gremio have finally agreed the terms of a transfer.
The report claims that Barcelona will pay €30m up front, plus another €10m in add-ons related to appearances and his first contract renewal.
Arthur, who has not featured for Gremio this year due to an ankle injury, will remain with the Brazilian club until December and will join Barcelona in January 2019.
Arthur has represented Brazil at under-17 and under-20 levels but has not yet featured for the senior side, although he did receive a call-up in September.