Friends and family waited all day on Tuesday for news of the centre-left politician and his wife Elke Büdenbender from a Berlin clinic, and around 6 pm they were informed that both patients were beginning to wake up after their surgeries, daily Bild said.
On Monday, Steinmeier, who is also a former foreign minister, made the surprise announcement that he would be taking time off until October to donate a kidney to his wife, who was suffering from what he called an “advanced kidney ailment.”
The 54-year-old said he planned to return to his duties sometime in October after recovering from the surgery.
The double procedure took all day, and doctors won't know if 48-year-old Büdenbender's body will accept her husband's kidney for a few weeks, Bild reported.
During Steinmeier's absence SPD deputy parliamentary group leader Joachim Poß will take over leading the party in the Bundestag.
Steinmeier and his wife have been married since 1995 and have a teenage daughter together.