The men, identified by Al-Jazeera as British-South African hostage Stephen Malcolm, Swede Johan Gustafson and Dutch national Sjaak Rijke, appeared in good health in the video which was not accompanied by audio.
The hostages were bearded, wore traditional flowing robes and their heads were covered by turbans. They were shown sitting on rugs in a desert area surrounded by armed men.
Al-Jazeera said in a statement that it conducted an "exclusive interview" with the hostages who gave a detailed account of their abduction in November 2011 and urged their respective governments to step up efforts to free them.
"The captives urged their countries to engage in swift and effective negotiations with the kidnappers to bring their turmoil to an end," according to the statement.
They also said "they were taken from their hotel in Timbuktu at gunpoint into an SUV vehicle and transported to unknown whereabouts. After that they were forced into a strenuous 24-hour journey," it added.
"Later the kidnappers promised that no harm would be done to the captives who told Al-Jazeera that they have been well treated."
According to Al-Jazeera the hostages were seized by Ansar Dine, an Islamist group affiliated to AQIM, along with a German national who was killed as he resisted his abduction.
In December AQIM claimed responsibility for the abductions and released pictures of the hostages.
In April it offered to free Malcolm if London allows radical cleric Abu Qatada to choose a country for his extradition, the US monitoring service SITE reported at the time.
For more than six years, Britain has been trying to deport Abu Qatada to Jordan, where he was convicted in absentia in 1998 of involvement in attacks.
AQIM is also holding six French citizens kidnapped from Niger and Mali.