The South African has seen his initial work permit to play in England turned down by the Home Office, but that decision is being appealed against and the hearing will take place early next week.
"It is all done," McCarthy told Marca.
"I will continue training for the rest of the week and on Saturday I will said goodbye to my team-mates.
"I remain with Vigo until the permit is done, something that will arrive on Monday or Tuesday."
Celta sealed a deal with Boro last week, with a clause stating that the Teesside club can buy him December for a fee of 16 million pesetas (£6.7 million).
McCarthy will be the third Vigo player to leave in a matter of days after the club let Chilean international Pablo Contreras and central defender Manolo join their La Liga rivals Osasuna on loan for the rest of the season.
Celta have now completed their 23 man squad for the season, which has meant a shock recall to the first team fold for Ecuadorian international Ivan Kaviedes, who was expected to be surplus to requirements this season.
