The Ganden Tripa or Gaden Tripa (tib. dGa’-ldan Khri-pa) ("Holder of the Ganden Throne") is the title of the spiritual leader of the Gelug (Dge-lugs) school of Tibetan Buddhism, the school which controlled central Tibet from the mid-1600s until 1950s. He is identical with the respective abbot of Ganden Monastery. The present head of the Gelugpa order is Khensur Lungri Namgyal, the 101st Ganden Tripa and not, as is often misunderstood, the Dalai Lama. The Dalai Lama is the temporal head of the Gelug school, a position of greater political authority but of lower spiritual rank.http://en.wikipedia.org/wiki/Ganden_Tripa
The Ganden Tripa is an appointed office, not a reincarnation lineage. It is awarded on the basis of competitive examination. Since the position is not a life-long one, there have been many more Ganden Tripas than Dalai Lamas to date (101 as against 14).
Either Tsongkapa (Tsong-ka-pa) (1357–1419), who founded the Gelug sect, or his successor, Gyaltsab Je (Rgyal-tshab-rje), may be considered to have been the first Ganden Tripa. (After Tsongkhapa's passing, his teachings were held and kept by Gyaltsab Je and Khedrub Je who were the next abbots of Ganden monastery. The lineage has been held by the Ganden Tripas–the throne-holders of Ganden Monastery.)
In January 2003, the Government of Tibet in Exile announced the nomination of the 101st Ganden Tripa. An excerpt from that press release gives his background:
The 101st Ganden Tripa, the Venerable Khensur Lungri Namgyel rinpoche was born in 1927 in Kham (eastern Tibet). Ordained at eight years old, after fifty years of meditative practices and studies he was elevated by H.H. the Dalai-lama as successively abbot of Gyutö Tantric College (in 1983), and as abbot of Ganden Shartse Monastic University (in 1992). In 1986 he was the special envoy of H.H. the Dalai-lama to the ecumenical meetings of Assisi in Italy convened by H.H. the Pope John Paul II. He is a French national and has been living in Paris, France for more than 20 years. He transmits the Buddhist teachings of his lineage in a Dharma Center, Thar Deu Ling which he founded in 1980.
The 100th Ganden Tripa, Venerable Lobsang Nyingma Rinpoche, has since retired and now resides at Dharamsala together with the 14th Dalai Lama.