A self-portrait of David Hockney standing before a work-in-progress while his friend and former assistant, Charlie Scheips, scrutinises the canvas has been acquired by the National Portrait Gallery.

The £148,000 purchase is the gallery's first painted self-portrait of Hockney. Completed two years ago, it was bought from funds raised by "gift aid" in which the public donates money on buying an admission ticket, as well as a fundraising gala marking the gallery's 150th anniversary.

The price was agreed by the artist as a goodwill gesture for the success of a recent exhibition at the gallery featuring 150 of Hockney's portraits, which ended in January this year and was one of the gallery's most successful, culminating in its first late-night opening.

While the National Portrait Gallery has an extensive collection of photographs by Hockney, as well as a self-portrait drawing and etching, this is the first painted portrait by the Yorkshire-born artist.

According to the gallery, it echoes the psychological intensity of Hockney's "double portraits" featuring couples or friends in the late 1960s and early 1970s.

"This time, however, the painting shows a triangular exchange of gazes between the artist, the model who observes the painting unfold, and, ultimately, the viewer," said a spokesman.

Painted from a series of figure studies which Hockney made from life in his Los Angeles studio, it has been exhibited only once before and now becomes a significant addition to the gallery's collection of artists' self-portraits.

It will be displayed in the gallery from 11 October, where there will also be two of the artist's most acclaimed works from the 1960s, Portrait Surrounded by Artistic Devices and I'm in The Mood for Love, painted while Hockney was a student at the Royal College of Art. Sandy Nairne, the gallery's director, described the purchase of the self-portrait as "one of the wonderful results of the 150th anniversary year."