The singer said he was "incredibly chuffed" by the success.
"Both tracks mean a huge amount to me so it really is amazing to see them go to the top of the chart together."
Sheeran`s comeback follows a "gap year" where he removed himself from social media, making space to write his third album, ÷ (Divide).
Fans were clearly hungry for new material, as the star set several streaming records over the course of the week.
Shape Of You`s bouncy, uptempo pop was the bigger hit, notching up 13.4 million streams - smashing the record Drake set last summer, when One Dance was streamed 8.9 million in a single week.
Castle On The Hill, built around a chiming, U2-style guitar riff, also beat Drake`s tally, with 11.07 million streams.
On Spotify, Sheeran also broke a global streaming record held by One Direction, whose single Drag Me Down racked up 4.76m streams in one day in August 2015.
Shape Of You was streamed 6.13 million times when it was released last Friday, increasing to 7.24 million streams on Monday.
