The prime minister's office said that the law will go into effect 120 days after the publication of regulations outlining how the reforms will be implemented.
Congress narrowly approved the bill earlier this month, Dow Jones Newswires reported.
The legislation, which has received mixed reviews from the private sector, was sent to Congress by the Finance Ministry.
Among the measures to increase coverage, the law will require workers under 40 years old to sign up with a pension fund, while also requiring independent workers who make more than 1.5 times the minimum wage to make contributions.
The private pension system, which includes four private pension funds, was established in 1993 and has registered about 5 million people.
The pension funds are AFP Horizonte SA, which is owned mainly by Holding Continental and Spain's Banco Bilbao Vizcaya Argentaria SA; AFP Integra SA, which is owned by Colombia's Grupo de Inversiones Suramericana SA; AFP Profuturo, whose main shareholder is a unit of Bank of Nova Scotia; and Prima AFP, which is controlled by Peru's Credicorp Ltd.