He was the first son of Almarhum Sultan Alaeddin Sulaiman Shah ibni Almarhum Raja Muda Musa (1893-1938) by Cik Puan Hasnah binti Pilong, a commoner wife. Named Tengku Alam Shah at birth, he was not expected to succeed as he had two elder half-brothers.
Tengku Alam Shah was proclaimed Sultan on 4 April 1938, four days after the death of his father. On 26 January 1939, he was crowned at Istana Mahkota Puri in Klang. Tengku Musa Eddin, then Tengku Kelana Jaya Putera, presided over the ceremony.
On 3 August 1957, by eight votes to one, Sultan Alam Shah was elected Deputy Yang di-Pertuan Agong of independent Malaya.
Sultan Alam Shah was elected second Yang di-Pertuan Agong on the death of Tuanku Abdul Rahman. His term of office began on 14 April 1960. On 30 July 1960 he proclaimed the end of the Emergency in Malaya.
Sultan Alam Shah died from an unidentified illness at Istana Tetamu in Kuala Lumpur on 1 September 1960, aged 62, the day fixed for his installation. He was interred at the Royal Mausoleum near Sultan Sulaiman Mosque in Klang, Selangor on 3 September 1960.
Sultan Hisamuddin Alam Shah was married at least twice:
- in 1920 to Raja Jemaah binti Raja Ahmad (1900-1973), a member of a junior branch of the Selangor royal family, who served as Tengku Ampuan of Selangor and Raja Permaisuri Agong
- in 1927 to Kalsom binti Mahmud (1913-1990), who was the mother to Tengku Ampuan Besar Bariah of Terengganu.
He was succeeded by his son by Raja Jemaah, Tengku Abdul Aziz Shah, as Sultan of Selangor, taking the title of Sultan Salahuddin Abdul Aziz Shah. Sultan Salahuddin later became the 11th Yang di-Pertuan Agong and also died while in office like his father.