It lies in the Bellingshausen Sea west of Palmer Land, Antarctic Peninsula from which it is separated by Marguerite Bay and George VI Sound.

Its insular nature was proven in December 1940, by a two-person sledge party composed of Finn Ronne and Carl Eklund of the United States Antarctic Service.

There exist some exposed nunataks and a few ice-free areas of significant size, including Ablation Point Massif.

These mountains, peaks, hills, and uplands are surrounded by a permanent ice sheet, which consists of glaciers that flow off of Alexander Island.

The northern side of Hodgson Lake is bounded by the Saturn Glacier, which flows east into George VI Sound, while the southern side of Hodgson Lake is bounded by the northern face of Citadel Bastion.

It was named by the UK Antarctic Place-Names Committee after Johannes Brahms, the German composer.

According to Hole, "The geology of Alexander Island can be attributed mainly to processes associated with the subduction of proto-Pacific oceanic crust along the western margin of the Antarctic Peninsula, from latest Triassic to Late Tertiary times."

The LeMay Group accretionary prism complex, along with plutonic and volcanic rocks, are prevalent along the western portion of the island.

Although it is dominated by deformed arkosic sedimentary rocks, it includes turbiditic greywackes, black mudstones, and conglomerates.

Sand dykes are found against this fault zone and in many other parts of the Fossil Bay Formation.