The engagement took place at the home of Ms Al Saif's father in Riyadh. It was announced on Twitter with four photos showing the couple together, with Prince Hussein's parents, King Abdullah II and Queen Rania, pictured alongside members of Ms Al Saif's family.
A statement issued by the court said Surah Al Fatihah, the first verse of the Quran, was read during the event, a common practice at an engagement.
Queen Rania also took to Twitter to share her happiness.
“I didn’t think it was possible to hold so much joy in my heart! Congratulations to my eldest Prince Hussein and his beautiful bride-to-be, Rajwa,” Queen Rania wrote.
On Instagram, the queen shared more photographs showing the royal couple embracing their future daughter-in-law with wide smiles.
The engagement comes a month after Prince Hussein's sister, Princess Iman, got engaged to Jameel Alexander Thermiotis.
Prince Hussein, 28, was named in honour of his grandfather, the late king Hussein bin Talal. A graduate of the British military academy Sandhurst, he holds the rank of captain in the Jordanian armed forces and can fly a military helicopter. He was officially named crown prince in 2009 by a royal decree.
He also holds a degree in international history from Georgetown University in the US and runs a number of charitable efforts through his Crown Prince Foundation.
Ms Al Saif was born in Riyadh in April 1994, Jordan's Roya News reported. She was educated in Saudi Arabia before moving to New York, where she studied at Syracuse University.
The family were inundated with well wishes from regional leaders. Saudi Arabia’s Crown Prince Mohammed bin Salman called Prince Hussein and imparted his best wishes, and UAE President Sheikh Mohamed made a congratulatory phone call to King Abdullah.
During the conversation, Sheikh Mohamed extended his best wishes to the family “prayed to Allah Almighty to grant Jordan's Crown Prince success and a happy life”, Wam reported.