The Wire and Luther star follows in the footsteps of David Beckham, Mel Gibson, Dwayne "The Rock" Johnson and Blake Shelton.
The British actor and star of The Wire, Luther and Mandela: Long Walk to Freedom tweeted a picture of the front cover and said he was "honoured and thankful", while also urging people to vote in the midterm elections.
Elba, who was revealed as the winner on Monday's The Tonight Show Starring Jimmy Fallon, follows in the equally sexy footsteps of previous winners including David Beckham, Mel Gibson and Dwayne "The Rock" Johnson.
Last year, country singer and The US Voice judge Blake Shelton took the title.
Telling People how he reacted to the news, the 46-year-old said: "I was like, 'come on, no way. Really?' Looked in the mirror, I checked myself out.
"I was like, 'Yeah, you are kind of sexy today'. But to be honest, it was just a nice feeling. It was a nice surprise - an ego boost for sure."
He also spoke about his awkward teenage years, saying he was picked on before he grew into his looks.
"I was very tall and skinny," said Elba, who is 6ft 3ins. "And my name was Idrissa Akuna Elba, okay? I got picked on a little bit.
"But again, as soon as I could grow a moustache, I was the coolest kid on the block. Grew a moustache, had some muscles, bonkers."
On Twitter, the star said: "Who'd have thought it! Thank you @people & all the fans for naming me #SexiestManAlive.
"I'm honoured & thankful. What's even more important is your vote in the midterm elections. Your vote can make a difference!"
Elba was among the favourites to take over Daniel Craig as James Bond before ruling himself out earlier this year, telling Sky News he was "having a laugh" over the rumours.
He has two children, and proposed to his model fiancee Sabrina Dhowre, 29, in February.