Brolin and Gyllenhaal, who are staying at a five-star hotel in Kathmandu, will play the lead roles in the film, named "Everest", which will focus on an ill-fated attempt to scale the world's tallest mountain in 1996.
Iceland's Baltasar Kormakur is directing the film, which tells the story of how eight climbers lost their lives when a rogue storm struck the mountain.
"A local agent applied for permission on behalf of Baltasar Kormakur to shoot 'Everest' and received the permission three days ago," communications ministry official Umakant Parajuli told AFP.
Parajuli said the team was permitted to shoot in the Himalayan nation for two weeks.
He declined to comment on whether the shoot would include a stint on the famed peak this month, when temperatures are expected to be at their lowest level annually.
File photo of actor Josh Brolin
British newspaper The Guardian reported last week that Gyllenhaal would play Scott Fisher, a US expedition leader who died in the disaster while Brolin will play Beck Weathers, an American doctor who survived the storm.
US mountaineering journalist Jon Krakauer, who accompanied the Everest climbers on their ascent, wrote about the tragedy in his 1997 bestseller.
Hundreds of climbers scale the peak every spring, while thousands more go trekking from Lukla, the nearest airport, to Everest base camp.
Last year, a brawl between three European climbers and Nepalese guides on Everest hit global headlines, raising concerns that the mountain had become too crowded in recent years with climbers eager to set new records.
