Coldstream and Duns had both applied - along with five others - after the Lowland League, which was only founded last year, invited applications.
Up to four places were available, but on Monday it was confirmed only two applications had been accepted - from Edinburgh University and Broomfill Sports Club in Glasgow.
League Chairman Andrew Waddell said, “The Board looked carefully at all the applications and decided that Broomhill SC Glasgow and the University of Edinburgh met our requirements most.
“It was a tough decision for the Board as each applicant was assessed on its own merit.
“Its very encouraging that so many clubs are aspiring to play in our League and have all started to take steps to achieve club licensing,.
“I am hopeful that the clubs who were not elected this time continue to work towards achieving their license and I am sure they will look to get elected next season.”
Coldstream and Duns both currently play in the East of Scotland League at Premier Division and First Division status.