Greatest Hits is the band's best-selling album to date, with total sales of over 25 million copies, making it one of the best-selling albums of all time. It reached number one on the UK Albums Chart, spending four weeks at the top and sold consistently well throughout the 1980s, becoming the fourth-biggest selling album of the decade. The single "Under Pressure", which was released the same week as Greatest Hits, also topped the UK Singles Chart.
As of November 2021, Greatest Hits has spent over 900 weeks on the UK Albums Chart, and has been certified 23× platinum with sales of over six million copies, making it the best-selling album of all time in the UK. Greatest Hits peaked at number eight on the Billboard 200 in November 2020, the second-slowest ascent to the top ten of the US album chart in history. Among the longest charting albums in the US, as of November 2020, it has spent over 400 weeks on the Billboard 200, and has been certified 9× platinum in the US. It has also been certified 15× platinum in Australia, 10× platinum in New Zealand, and 3× platinum in Canada. Following the release of the Queen biopic Bohemian Rhapsody in 2018, it re-entered the charts worldwide.