The incidents happened between 01:30 and 01:40 on Sunday 3 May at the Riego Street flats.
One woman was indecently assaulted and the other was assaulted.
A 25-year-old man was detained following a CCTV appeal and will appear at Edinburgh Sheriff Court on Friday.

HS2 Ltd, the company behind the rail link from London to northern England, last week said the redevelopment of the station would finish in 2033 - seven years later than planned.
Sir Keir Starmer, MP for Holborn and St Pancras, said those living nearby faced "decades of blight" from construction.
But the HS2 minister said the area would benefit from the redevelopment.
The first phase of HS2 will be between London and Birmingham and will be followed by a V-shaped section to Manchester and Leeds.
Euston is set to gain six new platforms and an additional concourse.
In a change to plans submitted two years ago, HS2 Ltd has proposed that the construction of five further platforms within the existing station should be delayed.
They would be ready for phase two of HS2 which will run from the capital to Leeds and Manchester in 2033.
HS2 Ltd said the changes meant the construction would be less intense.
But speaking to the Commons on Tuesday, Sir Keir rejected that: "We have had plans, amended plans and further amended plans for Euston.
"The only sensible plan is to abandon the project altogether.
"This plan, far from being an improvement on the other plans, is the worst of the lot and leaves my constituents with all of the pain and none of the gain.
"And I focus here particularly on the phased approach - it offers and sets up decades of blight with no assurance about when the project as a whole will be finished."
HS2 Minister Robert Goodwill said Euston needed to experience the same regeneration as King's Cross-St Pancras, also in north London.
He said: "Our Euston proposal is fully compatible with the redevelopment of the remaining Network Rail station and our proposals have been developed with Network Rail and (Transport for London)."
Replying to Sir Keir, Mr Goodwill said disruption for commuters also needed to be considered alongside disruption faced by residents.
He said reports suggesting there would be reductions in platform space were "not correct".
Mr Goodwill also said Transport Secretary Patrick McLoughlin was "very keen to see the resurrection of the Euston Arch".
Euston Arch, which was built in the 1830s, stood at the front of the station until it was demolished in 1962 when the station was rebuilt.
He said: "We think we know where the bits are, and indeed the Euston Arch Trust aims to reform the arch and it's for them to bring this forward through a local planning application, but we have a location in the new Euston Square Gardens for the arch to come forward."

Fatima Elomar, 31, was intercepted at Sydney Airport in May last year as she tried to board an international flight.
Cash, camouflage gear and medical supplies were found in her luggage.
In a brief court appearance, she pleaded guilty to supporting incursions into a foreign state with the intention of engaging in hostile activities.
Mohamed Elomar travelled to Syria and then Iraq in 2013 to fight with so-called Islamic State (IS).
Court documents reportedly detail text messages between the couple in which Ms Elomar begs her husband to return home for medical treatment after being shot.
Mr Elomar reportedly told his wife to prepare the children's passports so they could be together in Raqqa, Syria.
Mr Elomar, and fellow Australian Khaled Sharrouf came to public attention last year after they posted pictures of themselves posing with severed heads to social media.
One of those images showed Sharrouf's seven-year-old son holding up the severed head of a Syrian soldier.
It is believed Elomar died in June during an air strike on a convoy of vehicles near IS's self-declared capital of Raqqa.
The Australian government estimated in September that around 120 Australians were currently in Iraq and Syria to support IS and other terror groups.
A man has been charged after two women were attacked at student accommodation in Edinburgh.
[NEXT_CONCEPT]
Plans to redevelop London Euston as part of the high-speed railway line HS2 should be scrapped, an MP has said.
[NEXT_CONCEPT]
The wife of one of Australia's most notorious extremists, Mohamed Elomar, has pleaded guilty to supporting overseas terrorism.