Gabriel, who is also economy and energy minister, "will travel to Iran from July 19 to 21 with a small delegation of industry and science representatives," a ministry spokeswoman said in a statement to AFP.
Bilateral trade between Iran and Germany was once strong but fell as a result of the sanctions, declining from €4.7 billion in 2010 to €2.1 billion last year, according to German figures.
"There is great interest on the part of German industry in normalising and strengthening economic relations with Iran," especially after the nuclear agreement, the ministry has said.
Ulrich Grillo, head of the Federation of German Industries, has predicted two-way trade could surge to over €10 billions annually in coming years.
The German Chambers of Commerce and Industry said its head, Eric Schweitzer, had been invited along on the trip.
The agreement finalised in Vienna Tuesday aims to ensure the Islamic Republic does not obtain nuclear weapons.
In exchange, the oil-rich country of 78 million people will be given step-by-step relief from crippling international sanctions.
Grillo has pointed to pent-up demand in modernising Iran's industrial infrastructure, especially in the oil industry, which he said offered "big market opportunities" for German engineering companies.
Iran has the world's fourth largest oil reserves and the second in gas, meaning it has the biggest combined energy deposits.
Iran's oil ministry has announced it intends to attract up to $100 billion of foreign investment to modernise the sector, which has been underdeveloped for a decade.