The France international midfielder consented to move to Atletico some weeks back, but the two clubs had failed to agree terms.
One stumbling block was a disagreement over who would pay Luccin's previous club Paris Saint Germain the sell-on fee they were owed from the transfer.
However, after prolonged negotiations a deal has been struck and the 25-year-old will be officially presented by Atletico on Friday afternoon.
Luccin, who has played for Bordeaux and Marseille as well as PSG and Celta, has been looking to leave the Galician outfit since their relegation from the Spanish top flight last term.
No details of the transfer fee Atletico will pay have yet been released.