Gilmour's Rattle That Lock topped the official chart nearly 20,000 copies ahead of Del Rey's record, Honeymoon.
It is the guitarist's second solo number one, after 2006's On An Island. He last topped the charts in November, with Pink Floyd's The Endless River.
"It's thrilling to get a number one," he said. "We all want to hit the top spot, however long we've been at it."
Gilmour easily outpaced the competition in a big week for new releases. He was joined in the Top 40 by new albums from Keith Richards, Drake & Future and Gabrielle Aplin.
Cliff Richard scored his 43rd top 10 album with the greatest hits collection 75 at 75, which landed at number four.
And country singer Ryan Adams also made a new appearance at 19, thanks to his "cover album" of Taylor Swift's 1989.
The original was two places higher, marking its 48th week in the top 40.
In the singles chart, Justin Bieber spent a third week at number one with his tropical dance track, What Do You Mean? - which was streamed 3.2 million times over the last week.
The Canadian singer has a fight on his hands next week from Sam Smith's Bond theme, Writing's On The Wall, which has already  topped the iTunes chart after eight hours on sale.
Elsewhere in the top 40, Ellie Goulding scored her tenth Top 10 hit with On My Mind - the first single from her forthcoming album Delirium.
The song was originally released last Thursday, making it chart-eligible for 24 hours, during which time it reached number 165. This week, it climbed 158 places to land at number seven.
Other new entries included Runnin' (Lose It All), a collaboration between Beyonce and British producer Naughty Boy, which debuted at 11.
One Direction's Infinity, which became available on Tuesday to coincide with the announcement of the band's fifth album, Made In The AM, made its initial chart showing at number 36.
As well as Sam Smith, this week sees new singles from Little Mix and Rudimental featuring Ed Sheeran.
New Order, Disclosure, Chvrches and former Westlife member Shane Filan will all be vying to score the number one album.

Robert Dick was born in Tullibody, in 1811 and was apprenticed to a local baker after leaving school, aged 13.
But he began to study in his spare time, eventually becoming a world-renowned expert on the botany and geology of Caithness.
His achievements are being marked by the Tullibody History Group.
The group said the event would look at the legacy of a "remarkable, entirely self-taught man".
Despite a relatively humble upbringing - the son of an excise officer - his achievements were noted by some of the most prominent scientists of the day.
Sir Roderick Murchison of the British Association of Scientists was said to have remarked about him: "I found to my humiliation that this baker knew more of botanical  science - aye - 10 times more than I did."
And the well-known naturalist Hugh Miller, who received many fossils from Dick, wrote that "he has robbed himself to do me service".
In 1863, Dick had to sell part of his geological collection, which is now in the National Museums Scotland.
He continued his research, but in August 1866 he collapsed while gathering specimens in a quarry. He never recovered fully and died four months later.
The only memorial to him is in Thurso Cemetery, the Tullibody History Group said.
Members of the group hope to erect a new memorial to the man to mark the bicentenary of his birth this year, as well as publishing a book about his life.
An event on 27 August at the Tullibody Heritage centre would give a "fascinating insight into an unusual man", the group added.
Lana Del Rey has been denied her third consecutive number one on the UK album chart by Pink Floyd star David Gilmour.
[NEXT_CONCEPT]
The life of a 19th Century Clackmannanshire baker who went on to become a world authority on botany is to be celebrated.