The Spice Girls previously held the record for having the highest-placed debut entry on the US countdown, when their Spice LP hit No.6 on the Billboard chart back in February 1997.
According to Nielsen SoundScan figures, One Direction managed to sell 176,000 copies of Up All Night in its first week on sale.
Speaking of their achievement, Harry stated: "We simply cannot believe that we are No.1 in America! It's beyond a dream come true for us.
"We want to thank each and every one of our fans in the US who bought our album and we would also like to thank the American public for being so supportive of us."
Niall Horan continued: "We just found out that we are No.1 in America and as you can imagine, we are over the moon!
"When we got put together as a group, we couldn't imagine ourselves coming to America, let alone releasing our album here, so for us to be sitting at the top of the US album charts is unbelievable. We are so grateful to everyone who has supported us in the US."
BossSimon Cowellcongratulated the boys on their "incredible achievement", adding: "They deserve it. They have the best fans in the world"