The 20-year-old Emerson will join Barca on a five-year contract that runs through the 2023-24 season when he officially links up with the club on July 1.
Emerson, who turned 20 on January 14, has played one season at Mineiro scoring a goal and adding an assist for the club in 23 appearances, who finished sixth in the top-flight in 2018.
Previously, he had played for Brazilian side Ponte Preda, making just three appearances in the league for the club.
The right-back has also featured for Brazil at the youth levels and is currently with his nation's side at the South American U-20 championships, where he has started four of their five games.
In the Barca's statement over the transfer, Emerson was compared to former club star and felow Brazilian Dani Alves.
The move continues a busy January window for the Catalan club, which has seen multiple arrivals and departures.
The big transfer saw the Liga champions beat the likes of Manchester City and Paris-Saint Germain to the signing Ajax's Frenkie de Jong in a €75m move, which, like Emerson, will see the midfielder join the club in the summer rather than in the winter window.
However, Barcelona did land Kevin-Prince Boateng from Sassuolo to bolster the club's depth along the forward line along with Valencia's Jeison Murillo to do the same along the defence.
Both moves are loans but the club have the option to make the deals permanent.
In addition, Ernesto Valverde's side have loaned Denis Suarez to Arsenal and said goodbye to depth striker Munir El Haddadi earlier in the month in a €1m transfer to Sevilla as the player was set to leave the club for free in the summer.