Allen, who owns the painting, is shown sitting on the stool wearing a polka dot puffer jacket and boots revealing a tattoo on her left leg.
It will be on show for the next year and was unveiled the night before Allen begins a run of three gigs at the London Palladium theatre.
She added: “Nieves captured the feel of the album so brilliantly and I knew immediately it would make a very strong album cover.
“It seems to me the portrait reflects so many facets of the album – strength, power, vulnerability, determination and confusion, amongst many others – that it acts as a key to the whole listening experience. I love it.”
West End Girl was a huge success for Allen, earning her a Brit Award nomination and peaking at number two in the UK chart last year.
It was Allen’s fifth studio album and focused on her break-up with her ex-husband, US actor David Harbour.
Artist Gonzalez said she felt “enormously fortunate” to have been part of the album’s journey.
“I wanted it to be an intimate and direct image, but also powerful,” she said.
“To show her strength, her wisdom, through the eyes of the contemporary women that we are.”
National Portrait Gallery director Victoria Siddall said: “Our collection celebrates the people who have shaped our history and culture, and Lily Allen is undoubtedly one of the defining voices of her generation.”
The gallery’s collection includes likenesses of famous figures from William Shakespeare to Queen Elizabeth II, and from Charles Darwin to Adele.