The Mercury Prize showcases a range of genres by celebrating the best album by a British or Irish artist each year.
The musician said he "felt like I'm dreaming" as he was announced as the victor of the prize at a ceremony in London's Eventim Apollo on Thursday night.
Actor and DJ Idris Elba presented Sampha with the award after saying that English music is at the best it's ever been, ever. Grime artist Stormzy had also been well-regarded, with his debut album Gang Signs & Prayer positioned to make it consecutive wins for grime artists following Skepta's win for Konnichiwa a year ago.More news: US Congress sends anti-white supremacist resolution to Trump
Sampha's debut album Process received glowing reviews upon its February release, with the NZ Herald giving it five stars and declaring it "a debut album of breath-taking poise".
Sheeran, who is touring in the USA, sent a video message saying he was not expecting to be shortlisted but adding it was always a goal to play the Shepherds Bush Empire and have a Mercury-nominated album.
Applauding this year's Mercury Prize for its musical diversity, the band also picked Loyle Carner as the act they most wanted to see win. The Mercury Prize started out strong with Primal Scream's Screamadelica winning in 1992 and Suede's self-titled debut winning in 1993. Speaking at a press conference held shortly after the ceremony ended, Sampha again referenced his parents having dedicated the award to them from the stage.
Last year, Skepta won the prestigious award with his album Konnichiwa - the first grime artist to win since Dizzee Rascal in 2003 with Boy In Da Corner.