The singer sold almost 109,000 copies of his latest swing record during its first week on sale.
Williams has scored the landmark number one 57-and-a-half years after Frank Sinatra's Songs for Swingin' Lovers became the UK's first ever number one album.
Williams told The Official Charts Company: "I am over the moon that Swings Both Ways is Number one! And such an honour to be the 1000th album in that spot too, following Frank Sinatra who was the first person in that spot and my hero.
"Thanks to everyone who bought the record, see you all on the tour next year!"
Martin Talbot, the Official Charts Company's chief executive, commented: "Congratulations to Robbie Williams on claiming the 1000th Official Number One Album.
"He couldn't be a more suitable victor, both as one of the all-time greats of the Official Albums Chart (now tied with Elvis Presley as the male solo artist with most number one albums) and with his Swings Both Ways providing a beautiful symmetry with the very first number one in 1956, Frank Sinatra's Songs For Swingin' Lovers."
Meanwhile, Eminem's The Marshall Mathers LP 2 remains in second spot for another week, while Jake Bugg's second studio album Shangri La is a new entry at number three.
Celine Dion falls one place from three to four with her latest album Loved Me Back To Life. The record is Dion's highest-charting LP since 2002's A New Day Has Come.
Elvis Presley retrospective The Nation's Favourite Elvis Songs holds at number five and JLS's Goodbye - The Greatest Hits enters the chart at number six.
Lady Gaga's ARTPOP drops eight places from number one to nine on this week's countdown, while Little Mix's Salute falls four places to eight.
Michael Bublé's Christmas LP rises 23 places to number 14 as we draw closer to the festive period.
The other new entries in this week's chart are choirmaster Gareth Malone's Voices at number 23 and Gabrielle's Now And Always - 20 Years of Dreaming at 38.
Watch the music video for Robbie Williams's 'Go Gentle' below:
Source: Official Charts Company
View the latest Official Top 100 Album Chart