According to the Financial Times, Mr Obama promised a "very detailed plan" would be put forward soon after his team takes office on January 20th.
Ms Schapiro will lead a "crack down on the culture of greed and scheming" that helped to create and fuel the financial crisis, he added.
A former SEC commissioner, Ms Schapiro is a lawyer who has also chaired the Commodity Futures Trading Commission.
Yesterday (December 18th), she called for an "aggressive, systematic response" to reforming regulation in the US in order to restore investor confidence.
Former Nasdaq board member Alan Davidson told the newspaper the president-elect's choice could face serious challenges as she is "not known as a very good administrator" and the SEC is a "vehicle of the 1930s" in need of a complete revamp.
However, Richard Kidman of NYSE regulation said the experienced Ms Schapiro has previously demonstrated the ability to take a "demoralized organization" and "build it into a world-class regulator".