Bol was one of 22 players invited to the green room for the draft at Barclays Center in Brooklyn, but he was seen leaving his seat before returning just before deputy commissioner Mark Tatum announced the pick.
"The wait is over," Bol told ESPN's Maria Taylor after the selection. "I just want to prove everyone wrong and come out and be the best player I can be."
After a strong start to the college basketball season, Bol was as high as No. 5 in a mock draft by ESPN's Jonathan Givony in November. In Givony's last mock before Thursday's draft tipped off, he was projected to go No. 20 overall to the Boston Celtics.
Questions about Bol's effort and health apparently led to him slipping into non-guaranteed-contract territory.
Bol played in nine games for Oregon before suffering an ankle injury in mid-December and an eventual stress fracture in his foot that would sideline him indefinitely and end his collegiate playing career.
"My foot is 100 percent healed," Bol said Thursday night. "I just recently started to get back on the court about a month ago."
Nuggets president of basketball operations Tim Connelly said the team was "not concerned" about the reasons Bol fell in the draft.
"We feel very fortunate that he fell,'' Connelly said. "We were fortunate to add another young piece, a guy that we thought pretty highly of."
The No. 4-ranked recruit in the 2018 ESPNU 100 rankings, Bol was the highest-rated player to sign with the Ducks in school history. When on the floor, he didn't disappoint, leading the Ducks in points (21.0), rebounds (9.6), blocks (2.7) and 3-point percentage (52.0).
The first son of former 7-foot-7 NBA center Manute Bol of Sudan, Bol Bol's evolved game is highlighted by his versatility for his size and his ability to stretch the floor with his shooting.
Like his father, Bol Bol's shot-blocking potential and timing in the key has also impressed scouts.
His standout performance came in a late November loss to Texas Southern, when he scored 32 points and had 11 rebounds.
Denver's selection comes a year after it took another rehab project -- Michael Porter Jr. out of Missouri, the No. 14 selection last June who sat out the 2018-19 season.
Porter was considered a top-five selection before a back injury limited him to three games at Missouri in 2017-18. The 6-foot-10 Porter slid to the Nuggets, who felt his talent was worth the risk. A year ago, Porter underwent a second back surgery that sidelined him again. He is making big strides and expected to play in the Summer League next month.
"Fantastic,'' Connelly said when asked how Porter was progressing. "We want to temper expectations, but he looks healthier than he's been in a long, long time."
Porter's rebound from his back injury is a reason the Nuggets felt confident in taking a gamble on Bol.
"It made us more comfortable,'' Connelly said. "When you get a guy with the tools like Bol Bol, it's hard not to be excited."
Information from The Associated Press was used in this report.