Every portrait is about two things that are plain to see: likeness and presence. Depending on circumstances, a portrait can also be about something not necessarily evident but that can matter just as much: patronage. All three elements make a statement — about the sitter, about the artist — and all three come into play with the official portraits of Barack and Michelle Obama.

They were unveiled Monday morning at the National Portrait Gallery in Washington.

The NPG, which is part of the Smithsonian Institution, began commissioning presidential portraits in 1962. Subsequently, it began commissioning portraits of first ladies.

Kehinde Wiley’s life-size portrait of the former president shows him seated on the edge of a chair, wearing a suit (but with an open collar), gazing at the viewer, a characteristically reflective expression on his face. The likeness is spot on.

But neither pose nor attire nor appearance is what’s most distinctive about the painting. That would be the background, which consists of a wall of leaves, most of them green, with scatterings of lavender, pink, and yellow. “Pretty sharp,’’ Obama said at the unveiling.

Sharp isn’t quite the right word, though. Not edge but environment is the defining quality of the canvas. There’s a striking balance between Obama being out of place (he is notsitting in the Oval Office) and right at home. Even as his human presence visibly differs from his surroundings it somehow harmonizes with them. The apparent incongruity of the image invites extended looking, and the more you look the less incongruous it seems.

Amy Sherald’s portrait of Michelle Obama, also life size, doesn’t capture her features as well as Wiley’s portrait does those of her husband. But photography long ago liberated painting from any requirement for precise verisimilitude and let it strive for presence. And presence the portrait has in happy abundance.

Obama sits with her chin on her wrist, her other arm draped over a knee. She wears a sleeveless gown, displaying those famous Obama biceps. This woman’s strength is literal as well as figurative. The gown is mostly white, with bits of black and gray and pink and red (the black chimes with the spill of her hair).

The dress is a knockout, and so’s the painting. The gray-blue background emphasizes the sitter even more than the leaves do in her husband’s portrait. If anything, the starkness of Sherald’s background (softened by its cool hue) places a greater visual weight on the sitter — a weight the rendering easily bears.

The NPG presents the work of 20 or so artists to the president and his wife — and, some day, the president and her husband? — for them to make a final choice. Wiley and Sherald are the first African-Americans chosen to paint these portraits. That act of patronage makes a statement, just as the election of Obama as the first African-American president did. The statement would mean less if the portraits weren’t as good as they are. Of course the same could be said about the election as well as the selection.

Mark Feeney can be reached at mfeeney@globe.com.