Steinmeier - the first German foreign minister to visit the communist-ruled island nation since German reunification in 1990 - signed a series of political and economic agreements on day one of his trip.
Steinmeier welcomed the advent "of a new foundation for relations" between the two countries, according to state-run website Cubadebate.cu.
Steinmeier and his Cuban counterpart Bruno Rodriguez signed a joint declaration on cooperation and a memorandum on establishing a consultation mechanism between their ministries.
Also on Thursday, Steinmeier met with Havana Archbishop Jaime Ortega and toured parts of Havana's historic old city.
He also is scheduled to meet with several other ministers, business leaders and artists during his stay, but has no appointments with Cuban dissidents, according to his official schedule.
Cuba and Germany have remained trade partners despite strained political relations, with bilateral trade totaling €390 million in 2013, according to the latest available data.
Germany sent 124,000 visitors to Cuba in 2014 - fewer only than Canada and Britain.
The only other post-reunification visit to Cuba by a German minister came in 2001, when the then economy minister Werner Muller visited, according to German news agency DPA.
The European Union suspended relations with Cuba in 2003 over a crackdown on journalists and activists, but it began talks to restore them in April last year, aiming to persuade Havana to improve its rights record.
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