The El Tiempo daily wrote that among the emails accessed were several related to the possible purchase of some works of art, a deal which never went through.
Others dealt with school tuition payments for his daughter Maria Antonia, according to the newspaper.
El Tiempo said that Santos was made aware of the breach and that security officials were investigating who was behind it.
The revelation comes amid other allegations published in the press that an army intelligence unit had spied on the Colombian government's negotiating team at peace talks with FARC rebels in Cuba.
The talks, which began more than a year ago in the capital Havana, aim to put an end to the longest running conflict in Latin America, which has left hundreds of thousands dead in over 50 years.