Gift of the Givers, a disaster relief charity, was asked earlier this year by the families of Johan Gustafsson and Stephen McGowan, a South African citizen, to negotiate for their release.
In the videos, said to be recorded on October 20 and lasting less than a minute each, the two bearded men looked healthy and expressed the hope that they would soon be freed.
"I am safe and sound and in good health and I miss my family very much," Johan Gustasson says in the video. He says the date is October 20.
He thanked the government and Gift of the Givers for trying to secure his release.
The men were abducted in Timbuktu, northern Mali, when on a motorcycle holiday in November 2011 and have been held since by Al-Qaeda in the Islamic Maghreb (AQIM).
Gift of the Givers founder Imtiaz Sooliman told Swedish Radio News that their negotiator in Mali had received the videos on Tuesday but gave no indication of when the two could be freed.
"We have something in mind which we hope will work and we will have them home," he told Swedish Radio, although he would not reveal what plan they had in mind.
He said that the Swedish government had not been in touch about the video.
The last video of the two men was released in June.