I've learned that the style is called Empire. From Wikipedia:
An Empire silhouette is created by wearing a high-waisted dress, gathered near or just under the bust with a long, loose skirt, which skims the body. The outline is especially flattering to apple shapes wishing to disguise the stomach area or emphasise the bust. The shape of the dress helps to lengthen the body. The word "Empire" here refers to the period of the First French Empire.
The original empire line was seen on women from early Greco-Roman art when loose fitting rectangular tunics known as "Peplos" or the more common "Chiton" were belted under the bust, providing support for women and a cool, comfortable outfit suitable for the warm climate.
The last few years of the 1700s first saw the Empire dress coming into fashion in Western and Central Europe (and European-influenced areas), and it evolved through the Napoleonic era until the early 1820s, after which the hourglass Victorian styles became more popular. The style was often worn in white to denote a high social status (especially in its earlier years); only women solidly belonging to what in England was known as the "genteel" classes could afford to wear the pale, easily soiled garments of the era. Josephine Bonaparte was one of the traditional trend-setters or figureheads for the Empire waistline, with her elaborate, skilfully-decorated Empire line dresses. The complete and drastic contrast between 1790s styles (especially those of the second half of the decade) and the constricting and voluminous styles of the 1770s (with a rigid cylindrical torso above panniers) is probably partially due to the French political upheavals after 1789 (though there is not usually any very simple or direct correlation between political events and fashion changes). English women's styles (often referred to as "regency") followed along the same general trend of raised waistlines as French styles, even when the countries were at war.
The 1960s saw a revival of the Empire silhouette, possibly reflecting the less strict social mores of the era (similar to when the unconstricting 1920s "flapper" styles replaced the heavy corsetry of the early 1900s).