Amy-Blue captures the Back To Black singer looking down and is painted in hues of blue and black.
Cropped around her head, it was painted shortly after Amy died in July last year at the age of 27.
Artist Marlene Dumas, who is known for tackling subjects such as female beauty and pornography in her work, painted the portrait.
The gallery's curator said the picture's "rich, translucent blues... allude to Amy Winehouse's musical influences as much as to the melancholy details of her career."
The singer's father, Mitch Winehouse, said: "It is a fantastic piece of work and we are fascinated to know how Amy was seen and remembered by family, friends and artists of all kinds.
"With the Amy Winehouse Foundation, Amy is our inspiration and it is profoundly moving to find that she still inspires so many others too."
The small painting, purchased with the help of fundraising charity the Art Fund, does not feature the singer's famous beehive but shows Amy, who battled addictions to drink and drugs, wearing her distinctive black eyeliner.
The London gallery displays thousands of portraits and the Winehouse image, which has a wall to itself, is the first portrait visitors will see when they walk through the door.
The gallery's director, Sandy Nairne, said the painting, purchased from the Frith Street Gallery, was an "important portrait of an influential singer and songwriter".