The ailing 79-year-old president was rushed to a hospital in the Iraqi capital late Monday because of what was described as a medical emergency.
Iraqi Foreign Minister Hoshyar Zebari told The Associated Press on Thursday that doctors have determined the president had a "very serious stroke," and that he is showing signs of improvement.
"He is starting to regain his senses. He is able to feel pain, and this is a sign of progress," Zebari said.
Talabani's spokesman, Nasser al-Ani, said the president is able to move some of his limbs and communicate with simple signals, but is unable to speak.
The decision to move Talabani to Germany was made after his condition was stabilized and he began to show signs of improvement, according to Iraqi officials.
Vice President Khudier al-Khuzaie, an Arab Shiite, will temporarily assume Talabani's duties during his absence, Zebari said.
Iraq's parliament has the authority to choose a new president should Talabani's office become vacant. The Kurds would likely insist on retaining the presidency to maintain the government's power-sharing balance.
Iraq at one point had three vice presidents at a time, though one resigned last year and the other, Sunni politician Tariq al-Hashemi, fled the country after arrest warrants were issued against him.
In Germany, Foreign Minister Guido Westerwelle said Talabani arrived on Thursday morning.
"I can confirm that the Iraqi President Talabani is being treated in Germany. I send him heartfelt wishes for a quick and full recovery," Westerwelle said.
Berlin's Charite hospital, the German capital's largest, confirmed Thursday that Talabani had been admitted to its Virchow Clinic but wouldn't give any details on his condition nor what he was being treated for, citing patient confidentiality.
In a statement on its official website, Talabani's office said the treatment he underwent in Baghdad "provided the right conditions for the transfer of (Talabani) out of the country for follow-up treatment in Germany." It gave no further details on his condition.
"His health condition is stable and much better," said Firyad Rawndouzi, a senior member of Talabani's Patriotic Union of Kurdistan party.
The presidency of Iraq is largely a ceremonial role. Prime Minister Nouri al-Maliki is the head of government.
Talabani is overweight and has undergone several medical procedures in recent years, including heart surgery in 2008 and knee replacement surgery this year. He has previously received treatment in Germany.
Although his official powers are limited, Talabani is a senior Kurdish leader and has been a symbol of unity in Iraq. He has frequently used his position to mediate among Iraq's Sunnis, Shiites and Kurds, as well smaller minority groups.
Before he fell ill, Talabani was actively involved in trying to mediate in a crisis between Baghdad and the Kurds, who have their own fighters and considerable autonomy in their enclave in northern Iraq. The two sides last month moved additional troops into disputed areas along the Kurds' self-rule region, prompting fears that fighting could break out.
Last week, Talabani brokered a deal that calls on both sides to eventually withdraw troops from the contested areas, though there was no timetable for how soon the drawdown might take place.
Associated Press writers Sinan Salaheddin, Adam Schreck and Sameer N. Yacoub in Baghdad, and David Rising in Berlin contributed to this report.