Embiid had surgery last week to repair a stress fracture in his right foot, and could miss anywhere up to a full season depending on how rehabilitation goes.
He was not able to attend Thursday night's draft due to recovery from the surgery.
"It is different. Disappointed, I wish I could be there," Embiid said in an interview during ESPN's draft broadcast. "But I'm excited the Sixers took me. I still can't believe it. I started playing basketball so late, it just means that anything is possible. ...
"For my back injury, it hurt me. But I saw the doctors and they said I was going to be fine. And unfortunately this foot injury happened a week before the draft. But I believe in God and God knew what he was doing, I've always said that and I'm going to just keep praising him."
The versatile 7-footer had a fantastic freshman season with the Jayhawks, averaging 11.2 points and 8.1 rebounds while blocking 72 shots to earn Big 12 Defensive Player of the Year honors.
It was just Embiid's fourth season of playing organized basketball and he showed great strides with his post defense at Kansas. Through the first 14 games of the season, Embiid allowed 0.88 points per play and 50.0 field goal percentage as the post defender, according to ESPN Stats & Information. However, during the last 15 games, he allowed 0.55 points per play on 28.6 percent from the floor.
Embiid already had some health questions, mostly regarding a balky back. Now he's had foot surgery and could be out for up to six months.
But that didn't stop the 76ers from selecting him.
"Welcome to Philadelphia Joel," team CEO Scott O'Neil tweeted.
General manager Sam Hinkie and the rest the front office had gone silent since the draft lottery in May. The Sixers refused to release names of prospects invited to workouts, and media was booted from their practice facility for trying to catch a word with eventual No. 1 pick Andrew Wiggins during a secret workout.
The Sixers closed their practice facility to the media again Thursday night and did not make Hinkie or other team personnel available.
But they clearly like what they have in Embiid.
Embiid, who grew up playing soccer and volleyball, only decided to pursue basketball a few years ago. He started to blossom as a senior at The Rock School and ultimately chose to attend Kansas, where he arrived with less fanfare than fellow freshmen Wiggins and Wayne Selden.
Embiid hurt his back while landing awkwardly during a game late in the season, and missed the Jayhawks' final two regular-season games and the Big 12 tournament. He also missed a victory over Eastern Kentucky and a season-ending loss to Stanford in the NCAA tournament, after which he said that he would have been able to play had Kansas advanced to the second weekend.
"I think he'll fit great," Kansas coach Bill Self said. "They already have another big guy in Nerlens Noel who hasn't played yet because of injury. I guarantee when they're both healthy, it won't be easy to score near the basket."
Information from ESPN.com's Royce Young and The Associated Press was used in this report.