Vettel's victory at the Indian Grand Prix confirmed him as the 2013 champion, and also clinched Red Bull's fourth straight constructors' crown.
Vettel joins Juan Manuel Fangio, Alain Prost and Michael Schumacher as the only men to have won at least four championships - and he is the youngest to do so by six years.
"You've done it in style," Horner said on the radio as Vettel raced past the chequered flag. "Brilliant drive, you join the greats."
And an emotional Horner later said: "It is an amazing day. Words fail me for what Seb has done for the last four years.
"It is gutting on the day we win the constructor's championship that Mark Webber didn't finish and make it one-two.
"It was hugely emotional for everyone to see him cross the line. I said to him to try and do it in style and he did and to win this Indian Grand Prix for the third successive time is incredible.
"Let's take nothing away from Sebastian not just today but for the whole season. He knew his strategy was to get through the traffic and he did it. He worked his way back through the field and he created the opening for himself today."
Adrian Newey, Red Bull chief technical officer, said Vettel's character is key to his success.
"His feet are on the ground, he is just an ordinary kid who has not lost sight of who he is despite the success he has had," he said.
"He is very humble, very intelligent, he has that process like all the greats of being able to drive and be conscious of what is going on around him all the time. It has been a real pleasure to work with him.
"It is stunning. A few years ago, coming to Red Bull was a fresh adventure for a new team and it has been such an amazing ride. It is a great team within Milton Keynes, they are hugely dedicated - there are lots of people working so hard and this is the product of that."