Her appointment was made public in a royal decree on Saturday.
Princess Rima spent part of her childhood living in Washington DC.
She assumes the role at a difficult time, as Saudi Arabia tries to quell an international outcry over journalist Jamal Khashoggi's death.
Princess Rima will take over the role from the crown prince's younger brother, Prince Khalid bin Salman, who has been appointed as the country's deputy defence minister.
She follows in the footsteps of her father, Bandar bin Sultan al-Saud, who held the US ambassador post from 1983 until 2005.
Because of his role, she spent part of her childhood growing up in the US. She also got a Bachelor of Arts degree in Museum studies from George Washington University.
Since returning to Riyadh in 2005, Princess Rima has worked in both the private and public sector.
She has held several business positions, including as CEO of a retail company with Harvey Nichols Riyadh in its portfolio.
(Excerpts from BBC News)