Son of Philip Lutley Sclater and Jane Anne Eliza, the daughter of Sir David Hunter-Blair. He received his Master of Arts degree in Natural Science from Keble College, Oxford in 1885. He worked for two years as a Demonstrator at Cambridge and went on a collecting trip to British Guiana in 1886. He published about birds in the Ibis in 1887. In the same year he received an appointment as a deputy superintendent of the Indian Museum in Calcutta until 1891 when he joined the science faculty of Eton College. Sclater then took up the position of curator at the South African Museum, During his time in South Africa he continued his scientific writings, including the completion of the work 'Flora and Fauna of South Africa. In 1906, following a dispute with the Museum's board of trustees, Sclater resigned as curator. He travelled through Mombasa, Lake Victoria, Khartoum and Cairo before returning to England. He then moved to Colorado Springs, Colorado, which had been founded by his wife's brother-in-law, General William Jackson Palmer. Palmer offered Sclater a small estate outside the city and a professorship at Colorado College where he helped in reorganising the museum. When the general died in 1909, the couple returned to England.
From 1909 Sclater became curator of the Bird Room at the Natural History Museum. While working there he compiled the 'Systema Avium Aethiopicarum' (1924-1930). He worked there until his death.
In 1912 Sclater published 'A History of the Birds of Colorado' in two volumes. During World War One he volunteered for the Soldiers' and Sailors' Families Association.
Sclater was editor of 'Ibis' from 1913-1930, editor of the Zoological Record from 1921-1937, President of the British Ornithologist's Union from 1928-1933, and Secretary of the Royal Geographical Society 1931-1943. In 1930 he was awarded the Godman-Salvin God Medal. Known mainly for his work with birds, Sclater also described several new species of amphibians and reptiles. Four new species of snake were described by him in a single paper in 1891.
It was at Eton that he met his future wife, Charlotte Mellen Stephenson, an American divorcee whose two sons attended the school. They were married at St George's Cathedral in 1896. Both his stepsons were killed in action during World War One. In 1942 Charlotte died of injuries sustained during the bombing of London. In 1944 Sclater died at St George's Hospital, two days after a bomb fell on his home.