The Manresa-born defender, formed at La MasĂa, arrives on a permanent transfer for a four-season deal, though Barcelona have retained a percentage of any future sale in a structure similar to the one used when Ăscar Mingueza left for Celta's first team several years ago.
Olmedo, 20, is a Spain Under-19 international who spent time training with Hansi Flick's first-team squad last season, and made 15 appearances for Barca AtlĂštic before a meniscus operation cut short his campaign.
"Alexis stands out for his defensive solidity, dominance in the air and ability on the ball," the club said in a statement. "This signing allows Celta Fortuna to add a player with great potential and personality to the squad, who fits perfectly into the puzzle Fredi Ălvarez is putting together for the team's debut in the second tier in a matter of days."
Standing at 1.87m, Olmedo can also play at right-back, and will compete for a starting role alongside Quique Ribes, Pablo MeixĂșs, Seynabou Ndiaye and Joel LĂłpez in Celta's B side.
His arrival follows that of Paraguay international Hugo Cuenca, a Milan academy graduate who joins on loan from Genoa with an option to buy worth âŹ1m, as Celta moves to strengthen a squad that began pre-season with only 14 contracted filial players and ten youth-team players.
The defender is available to feature in Saturday's friendly and is expected to be involved when Celta Fortuna begin their Segunda DivisiĂłn campaign away at CĂĄdiz.
Celta have used a similar recruitment approach with Barcelona before, most notably with Mingueza, who progressed through the same pathway before establishing himself in Vigo's first team and later moving on to Crystal Palace.
Sporting director Marco GarcĂ©s and Ălex Otero, who oversee the club's B-team recruitment alongside Fredi Ălvarez's coaching staff, see Olmedo as a similar long-term project, with the versatility to play as a full-back adding further value to his profile as he begins life away from Catalonia for the first time in his career.