The group, the first wave of Cuba's biggest release of jailed dissidents since 1998, have expressed their joy at being released.
"You can imagine how a man in prison for seven years, including 17 months in solitary, must feel," said Garcia.
The prisoners were accompanied by members of their family, Garcia said.
The Catholic church has taken an increasingly public role in relations between the government and the opposition since the death of a jailed dissident hunger striker in February.
PJ Crowley, a spokesman for the US state department, said: "We welcome the release of seven political prisoners by the government of Cuba and the announcement by the Archbishop of Havana that additional prisoners could be released in the coming months.
"We applaud the efforts of the Cuban Catholic church, Spain and others who have worked towards the release of prisoners of conscience from jail in Cuba."
Restrictions on Cuba
Stephen Wilkinson, the director of the Centre for Caribbean and Latin American Studies at London Metropolitan University, said that the release of the prisoners came at a key diplomatic moment.
"The timing is acute because at the moment the European Union has put into abeyance its restrictions on Cuba, the so-called common position, and also in the United States there is a bill going through congress that would relax the embargo on trade and tourism," he said.
"This release of prisoners at this moment will assist them in both places that are trying to argue for an easing of the pressures on Havana ... It says to them 'now we have released these prisoner what are you going to do for us?'"
The detainees were among 75 political dissidents arrested in a 2003 government crackdown that resulted in lengthy prison terms on treason and other charges.
They have been serving sentences ranging from 13 to 24 years for violations of Cuban laws aimed at curbing opposition, and what the government views as subversive activities.
Church officials announced on Thursday the names of the first five prisoners to be released, and said all had accepted asylum in Spain, as did those on a list of 12 announced on Saturday.
"These people are forced to leave because if they wanted to stay in Cuba, they would remain under a totalitarian regime and go back to being incarcerated"
Angel De Fana,
Neither the church nor the Cuban government has said whether agreeing to exile is a requirement of release, with Ortega describing exile as an "option".
"The Vatican is probably the government that has the strongest relationship with Havana at the moment and within the island, the Catholic church has had a greater role as an interlocutor," Wilkinson said.
Raul Castro has pledged that the dissidents would be allowed to return to Cuba with special permits, and would not lose their property in Cuba as is normally the case for emigrants.
While the government's promise to release prisoners has raised hopes on the island, praise from outside has been grudging, particularly from human rights groups and the US.
"This does not imply a change in the repressive regime," Angel De Fana, the Miami-based director of the Plantados group of former political prisoners, said.
"These people are forced to leave because if they wanted to stay in Cuba, they would remain under a totalitarian regime and go back to being incarcerated."
Hillary Clinton, the US secretary of state, praised the development on Thursday, but described the releases as "overdue".
Amnesty International, the UK-based human-rights group, said it would continue to campaign for all of Cuba's prisoners of conscience to be freed and sent home immediately.