The couple, identified only as technician Johannes H. and his wife Sabine, then both aged 35, and their three young children were abducted in June 2009 in northern Yemen.
Two of the children, both girls, were freed in May 2010, but the parents and their then one-year-old son have since died, the father's brother-in-law, Christian pastor Reinhard Poetschke, told AFP, citing a letter from the foreign ministry.
The family was abducted along with several other foreigners by kidnappers believed to have links to Al-Qaeda.
The two girls, now aged eight and 10, live with relatives in the family's home state of Saxony in eastern Germany.