Western Stars - The Boss's 19th studio album - racked up 25,000 more combined sales than Madge's Madame X, which had to settle for second place.
The two new entries saw last week's chart-topper, Lewis Capaldi's debut album, knocked down to three.
In the singles chart, Ed Sheeran and Justin Bieber's I Don't Care held onto the top spot for a sixth straight week.
Taylor Swift claimed the week's highest new entry with You Need To Calm Down, which entered the chart at number five.
Little Mix have the only other new entry in this week's Top 10 with Bounce Back, the girl group's first release since leaving Simon Cowell's Syco record label.
The song incorporates elements from Back to Life, a chart-topper for Soul II Soul in 1989.
Western Stars - Springsteen's first album of new material since 2012 - is now the 69-year-old's 11th UK chart-topper.
That's one less than Madonna has achieved over a 35-year career that has seen her notch up the most UK number one albums by a female artist.
The promotion trail for Madame X has taken the 60-year-old singer from the Billboard Music Awards in Las Vegas to the Eurovision Song Contest in Tel Aviv.
Madonna's last studio album, 2015's Rebel Heart, also made its UK debut at two on its first week on sale.
British four-piece Bastille were another top five new entry with their third studio album Doom Days, which entered the chart at four.
That was one space ahead of Joy Division's Unknown Pleasures, the 40th anniversary reissue of which saw it attain a Top 40 placing for the first time since its 1979 debut.