The move reinstates the presidential term limit in place before 2005, when Colombia adopted a constitutional reform backed by Uribe that enabled him to seek a second four-year term the following year.
Santos, an Uribe protege who broke with his one-time mentor after succeeding him in 2010, was himself re-elected last year but vowed to do away with the practice.
The new measure, adopted Wednesday night as part of a broader package of government reforms, was approved over objections from the opposition Democratic Center party led by Uribe, who is today a senator.
Surveys found more than 70 per cent of Colombians backed the proposal to ban presidential re-election altogether.
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Interior Minister Juan Fernando Cristo welcomed the new measure, saying it would fight "the temptation to abuse power."
Since leaving office, Uribe has become one of Santos's most vehement critics, notably over the peace talks his successor is holding with the Revolutionary Armed Forces of Colombia (FARC).
Santos led an aggressive campaign against the Marxist guerrillas as Uribe's defense minister, and infuriated his former boss when he changed course and opened talks with them in November 2012.