The artist collaborated on both Robin Thicke's 'Blurred Lines', which secured the top spot with sales of over 1.47 million copies, and the second place entry 'Get Lucky' by Daft Punk.
The French duo's track, which also featured Chic's Nile Rodgers, sold 1.3 million copies during 2013, according to The Official Charts Company.
Williams also scored the final number one single of 2013 last week with his single 'Happy' from the Despicable Me 2 soundtrack.
Williams said of his success: "I'm humbled by all of the love the UK fans have shown. But, when you are working with incredible talent like The Robots and Robin, great things are bound to happen."
Meanwhile, Avicii landed the third biggest-selling single of the year with his debut number 1 'Wake Me Up'. The song also holds the title of the fastest-selling track, having shifted 267,000 copies in the first week after its release in June.
Passenger, real name Mike Rosenberg, claimed number four with 1.03 million copies of his single 'Let Her Go' purchased in 2013.
Rosenberg revealed his joy over his "surprise" success, saying: "It feels wonderful but completely ridiculous if I'm honest!
"For the last five years I've been busking and playing tiny gigs in pubs, so for one of my songs to suddenly get so popular is not only a dream come true, but also a huge surprise."
The top five is completed by 'La La La' by Naughty Boy ft Sam Smith, which has sold over 941,000 copies since its May release.
The British Phonographic Industry released figures yesterday (December 31) which revealed that the Arctic Monkeys, Bastille and Daft Punk were the most-streamed artists of 2013.
The top ten biggest-selling singles in the UK in 2013 are below: 1. 'Blurred Lines' - Robin Thicke/ Pharrell Williams/ TI 2. 'Get Lucky' - Daft Punk ft Pharrell Williams 3. 'Wake Me Up' - Avicii 4. 'Let Her Go' - Passenger 5. 'La La La' - Naughty Boy ft Sam Smith 6. 'Roar' - Katy Perry 7. 'Thrift Shop' - Macklemore/ Ryan Lewis/ Wanz 8. 'Just Give Me A Reason' - Pink ft Nate Ruess 9. 'Counting Stars' - One Republic 10. 'Mirrors' - Justin Timberlake
Model Emily Ratajkowski: Blurred Lines video is 'the bane of my existence'
Emily Ratajkowski, the model and actor who became famous after starring in the video for Robin Thicke and Pharrell Williams’s controversial hit Blurred Lines in 2013, has called the video the “bane of my existence”.
In an interview with InStyle magazine the model, who has since won roles in Gone Girl and EDM flick We Are Your Friends, said whenever “anyone comes up to me about Blurred Lines, I’m like, ‘Are we seriously talking about a video from three years ago?’”
The video, in which she appeared naked, and the song were accused of glorifying rape culture, and some clubs and university campuses banned it.
Ratajkowski also said she “wasn’t into the idea” of the video in the first place and that she thought that she “came off as a bit annoyed” in the video.
She added that she did not see why a “woman’s naked body is so controversial in our culture”.
“My mum taught me to never apologize for my sexuality,” she said.
“My dad never made me feel embarrassed. I also don’t think I’ve ever had an awareness of my own body as being super-sexual. It was always just my body.”
The song also was the subject of a legal battle with Marvin Gaye’s family being awarded $7.4m because of similarities between the hit and Gaye’s track Got to Give It Up.