[3] The town formed around a church, which belonged to the Premonstratensian Abbey Lac-de-Joux (L’Abbaye) and burned down in 1251.

After the breaking up of the Ancien régime the town was a part of the canton Léman from 1798 to 1803 during the Helvetic Republic.

The chapel which had been built on the ruins of the medieval church was cleared away during the building of a school house in 1899.

[5] The municipality is located at the foot of the Jura Mountains near the Col du Marchairuz road.

Saubraz is located at an elevation of 687 m (2,254 ft) above mean sea level (AMSL), 13 km west of the city of Morges.

It is a farming village sprawled across a plateau in the Jura Mountains between the valleys of Saubrett in the south and Toleure in the north.

The creek Saubrett and its tributary Toluere drain the eastern part of the area into the Aubonne river.

The plateau Saubraz is located between the two creeks; it gradually rises to the Jura Mountains in the northwest.

The highest point in Saubraz is located at 810 m (2,660 ft) AMSL at the foot of Mont Chaubert.

The blazon of the municipal coat of arms is Per pale Gules and Or, overall a Crane Argent, in Canton a Mullet of Five of the second.

[8] The age distribution, as of 2009[update], in Saubraz is; 62 children or 17.9% of the population are between 0 and 9 years old and 48 teenagers or 13.9% are between 10 and 19.

[9] The historical population is given in the following chart:[3][13] In the 2007 federal election the most popular party was the SVP which received 48.52% of the vote.

Even today agriculture plays an important role, as animal husbandry, dairy production and farming are the dominant occupations.

In the tertiary sector; 3 or 42.9% were in wholesale or retail sales or the repair of motor vehicles, 1 was a technical professional or scientist, 2 or 28.6% were in education.

[9] From the 2000 census[update], 35 or 17.7% were Roman Catholic, while 119 or 60.1% belonged to the Swiss Reformed Church.

In the Vaud cantonal school system, two years of non-obligatory pre-school are provided by the political districts.

The canton's primary school program requires students to attend for four years.

[16] Saubraz is located away from the larger thoroughfares; the main access road comes from Aubonne.

Saubraz is connected to the public transport network, by way of the postal service’s routes, which run from Gimel, via Bière, to L'Isle.