South African Stephen Malcolm McGowan and Swede Johan Gustafson were abducted in Timbuktu, northern Mali, in November 2011 and have been held since by Al-Qaeda in the Islamic Maghreb (AQIM).
The film appears to have been shot in early April, according to McGowan's family, around the time that a Dutch hostage kidnapped with the pair was rescued in a raid by French special forces.
The 19-minute clip, uploaded to YouTube, shows McGowan and Gustafson sitting by the roadside in a forested glade with their wrists bound.
McGowan and Gustafson, heavily-bearded and dressed in tunics, appear in good health in the video, entitled "A Trip to Interview Two Prisoners".
Its release was announced by Mauritania's Sahara Medias yesterday but the news agency said it was unable to show the footage on its website because of technical difficulties.
The video is not dated, but McGowan is shown wishing his mother a happy birthday "for two weeks ago" and his wife a happy wedding anniversary "for last week".
AQIM was among several jihadist groups that took control of Mali's north in 2012 before being ousted by a French-led military operation launched in January 2013.
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