The 18 and 19-year-old were leaving their student accommodation, near Melrose Gardens, when a man approached them.
He threatened them with a weapon before grabbing one of the student's handbags and a mobile phone.
Police said the robbery took place between 11pm and 11.20pm on Monday.
The suspect is described as white, around 5ft 8in, of slim build, with a shaven head.
He was wearing a dark coloured hooded top, which was zipped up and obscuring his face.
PC David Adam said: "This was a very frightening experience for the young women concerned.
"The area which the robbery occurred is densely populated, and is a popular area for students.
"I am confident that we may be able to glean some information from the area and witnesses.
"We'd like to reassure the local community that we are working hard to identify the person responsible for this robbery."
Anyone with any information is asked to contact police on 101.