The purchase has been pending for more than 18 months, and the approval means that the transaction will be completed ahead of a July deadline set by NXP.
Qualcomm and NXP have not officially confirmed the report, which appered in Blomberg and earlier in the South China Morning Post.
China's review of Qualcomm's largest-ever acquisition follows a recent settlement of Chinese ZTE with the U.S. Commerce Department over the company's business practices. However, the Senate lawmakers are still pushing to keep stiff sanctions on the company, leaving the agreement's prospects unclear.
Qualcomm had promised investors that it would have the deal closed by the end of 2017. Buying NXP will help the company diversify its sources of revenue, as the Dutch company has a strong presence in the growing market for automotive chips.