The Official Charts Company reports the singer's track "Problem" ft. Iggy Azalea appears on the chart as having sold 113,000 copies, 106,0000 of which where purchased and 712,000 were streamed.
The new Official Singles Chart lists singles based on the streaming of songs in services like Spotify, Deezer, Napter, O2 Tracks, rara, Xbox Music and Sony's Music Unlimited in addition to sales. One hundred streams of at least 30 seconds are considered one purchase for listing purposes.
The streaming feature was first included last week and the first Top 40 to include the data was unveiled Sunday.
"Landing her first Number 1 on the Official Singles Chart is an incredible achievement and another benchmark in the continued global success of Problem," said Grande's maganer Scooter Braun.
"Problem" is Grande's first single to top the U.K. charts.
X Factor star Ella Henderson holds the second place on the list for her debut single "Ghost" and British singer Ed Sheeran's new album x -- pronounced "multiply" -- has topped the album chart for a second consecutive week, with all 12 tracks appearing in the top 100 singles.