The village of Budy was shown on Schubert's map of 1826–1840. However, it is signed there as "Lady", possibly a misprint or an old name that was later changed to Budy.
Further in written sources the village is mentioned in 1905, not as a settlement, but as a forest fire department of Osowiec parish, where 1 inhabitant lived.
In 1919–1939 it was part of Poland, as part of the village Paluszczyn, Ilow commune. In 1930 there were already 16 households in the village and a school.
In 1939 the village became part of the BSSR. From 15.01.1940 it was included in Antopol district, Brest region. From 12.10.1940 it belonged to Detkowicze village council and had 118 inhabitants.
During the Great Patriotic War 5 inhabitants of the village died, 4 of them at the front. Since 08.08.1959 the village is listed in Drohiczyn district. It had 97 inhabitants, in 1970 — 105 inhabitants, in 1995 — 24 yards and 43 inhabitants.