Ulla Schmidt, Germany's health minister, said: "I think a lot of people can, literally, breathe easier now."
Schmidt added that "so long as a sufficient number of rooms is available, special rooms can - but don't have to be - designated for smokers."
The ban would apply to buses, trains, stations, aircraft, federal courts, ministries and other government buildings.
German efforts to ban smoking in all public places suffered a setback last December amid concerns over who is responsible for a possible ban - the federal government or the country's 16 states.
Last Friday, state officials agreed in principle on a smoking ban in public buildings, including theatres and cinemas.
However, the states left open the possibility of allowing separate smoking rooms in restaurants, and at least two regional governments would like to allow exemptions for bars.
"We have done what we can at the federal level," Schmidt said.