The announcement named the two man as Hasan Zemiri and Adil Hadi al-Jazairi Bin Hamlili and came on the eve of what was once President Barack Obama's target date to close the notorious facility.
But a political firestorm at home over the Obama administration's plans to house some of the terror suspects on US soil and the reluctance of foreign allies in released detainees have dealt a blow to his landmark promise.
Some 196 detainees remain at the US military prison in southern Cuba, including dozens already cleared for release, down from around 250 when Obama took office. Most have been held without charge or trial.
Slovakian Foreign Minister Miroslav Lajcak said Tuesday that his country would accept three prisoners from the jail "as a gesture of alliance and solidarity.''
US lawmakers and the Defense Department have warned that a growing number of former Guantanamo detainees are joining militant groups to fight against the United States.
A Pentagon report in April found that about 14 percent of former Guantanamo inmates either had or were suspected of having ties to militants.
Obama suspended the transfers to Yemen after it emerged that the Nigerian man accused of trying to blow himself up aboard a US-bound airliner carrying nearly 300 people was allegedly trained by an Al-Qaeda affiliate in Yemen.
But in its statement about the latest transfers, the Justice Department said "the United States coordinated with the government of Algeria to ensure the transfers took place under appropriate security measures.''
Hours before the transfer was announced, Obama's Republican foes unveiled legislation to restrict his ability to transfer Guantanamo detainees overseas, in the latest possible setback to his plans to close the facility.
The Detainee Transfer and Release Security Act of 2010 aims to require Obama to certify that a detainee's destination country is not a state sponsor of terror, has control over its territory and does not tolerate safe havens for extremists like Al-Qaeda.
The measure also called for the president to certify that there has been no confirmed case of a Guantanamo Bay detainee engaging in extremist activities after being released to the proposed destination.
The legislation was unlikely to attract enough support from the president's Democratic allies to become law.