Sources had told ESPN on Sunday that an initial transfer fee would be around $4 million with incentives possibly taking the final cost to around $7m.
"We are excited for Eduard in the next step of his career," LAFC co-president & GM John Thorrington said in a club statement. "Since he arrived in our first season, Eduard has been a leader both on and off the field. His contributions in building LAFC have been immense, and we are grateful for how he has represented the club. Eduard developed into an MLS All-Star and Best XI player in his time in LA, and it is gratifying to see him move on to perform for a team that won the 2020 and 2021 Copa Libertadores."
Atuesta had been a mainstay in LAFC's midfield since arriving on loan from Independiente Medellin ahead of the 2018 season.
After impressing during that campaign, LAFC acquired Atuesta on a transfer, and the Colombian has made a total of 109 league, cup and playoff appearances with nine goals and 23 assists.
During that time led LAFC to the Supporters Shield in 2019, and made the league's Best XI that same year. He was also named an MLS All-Star in 2021.
At international level, Atuesta has played for Colombia's under-20 and U23 teams, but has yet to make an appearance at senior level.
LAFC has also traded Pablo Sisniega to Charlotte for $50k in general allocation money (GAM), while Franco Escobar arrived from Atlanta United for $250k in GAM. Incentives could take the deal up to $600k.