Portuguese President Anibal Cavaco Silva accepted Prime Minister Pedro Passos Coelho's nomination for the university professor to take the post on Tuesday, Xinhua reported.
Rodrigues, 60, will be sworn in on Wednesday by President Cavaco Silva at the presidential palace in Lisbon. She will be the first woman to head the Portuguese ministry.
She was elected after Miguel Macedo stepped down on corruption charges
Rodrigues was a professor at the Faculty of Law at the University of Coimbra in northern Portugal, and also managed the faculty from 2011 to 2013.
Miguel Macedo resigned on Sunday just three days after 11 people were detained for their suspected involvement in the golden visa scheme for wealthy foreigners.
The golden visa scheme started in 2012 and allows foreign investors the right to reside in Portugal as well as visa-free travel in the Schengen zone if they meet several requirements like investing a million euros in capital, purchase real estate worth of 500,000 euros or creating at least 10 jobs in the country.