Emilio Botin, a controversial figure who had steered the eurozone's biggest bank by capitalisation through Spain's financial crisis, died overnight aged 79, the bank said in a statement.
The appointment of his daughter, who became the first woman to lead a major bank in Britain when she took over as chief executive of Santander UK in 2011, marks the fourth generation of the family to chair the lender.
The board said the Harvard-educated 53-year-old was the "most appropriate person, given her personal and professional qualities, experience, track record in the group and her unanimous recognition, both in Spain and internationally".
He took over from his father as Santander's executive chairman in 1986 and expanded it, fusing it over time with entities such as Britain's Abbey National and others in Latin America.
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Spain's conservative Prime Minister Mariano Rajoy paid tribute to Botin today, calling his bank "a great ambassador for brand Spain".
Botin's sudden death, weeks before his 80th birthday on October 1, "was a surprise and a great blow", Rajoy told reporters at parliament.
Leading the international expansion of his bank, named after its hometown in northern Spain, Botin would entertain foreign journalists by joking about his strong Spanish accent when he spoke English.
A patron of science and the arts, he enjoyed the smooth image of a neatly-groomed bald executive in his trademark red tie, known to his managers as "El Presidente".
He kept a collection of art and groves of olive trees at Santander's vast headquarters on the outskirts of Madrid and was a keen golfer and fan of Formula One racing.