The deal is for two years, a league source told ESPN NFL Insider Adam Schefter.
Moreno is expected to miss the rest of camp, and Buckhalter about a week.
In a somewhat surprising twist, the Broncos released Kolby Smith, the most experienced of their current crop of backup running backs who had received a heavy workload through the first four days of camp.
Before White can suit up for the Broncos in the regular season, though, he has to miss the opening four games for violating the league's substance-abuse policy.
He remains eligible to practice and play in preseason games.
And while Broncos coach Josh McDaniels has made it his mission to bring in players with high character, he's willing to offer second chances.
"Had a long talk with him and really discussed the future," McDaniels said after practice Wednesday night. "We're going to judge him and make our judgments on LenDale White going forward as a Denver Bronco.
"Everybody makes mistakes."
Once practice finished, White walked off the field and straight into the team facilities without stopping to talk.
White grew up in Denver and played for USC, where he rushed for 3,159 yards and established school and Pac-10 Conference records with 57 total touchdowns, including 52 rushing.
He was selected in the second round of the 2006 draft by Tennessee, spending four seasons with the Titans.
White has had issues with his weight during his career. He ballooned to about 265 pounds with the Titans, before shedding the weight heading into camp last summer.
In 2009, Chris Johnson emerged as the Titans' top tailback, becoming a 2,000-yard rusher. Basically, White became expendable, the tandem once known as Smash and Dash broken up.
White was traded to Seattle for draft picks in April and showed up with the Seahawks, tipping the scales at a robust 219 pounds.
But he couldn't make it work there, despite being reunited with coach Pete Carroll, whom he starred for at USC. He was released in May after the Seahawks grew concerned over his work ethic.
The 25-year-old White is currently listed at 235 pounds in a release sent out by Denver.
The Broncos have been so thin at running back in camp that fullback Spencer Larsen found himself getting some reps in the morning session Wednesday.
After the night session, McDaniels said he's not worried about the depth at tailback. That's why the team simply swapped one running back for another.
"We just felt like we needed to upgrade the position," McDaniels explained. "We'll see what we have with LenDale."
"He's a very humble person now, I think," McDaniels said. "He's gone through some adversity in his life and his career. We'll see if this isn't a good place and a good fit for him to try to recoup what he had just a year ago or two years ago.
"We're just going to work with him, do our job and try to get him ready to play and play good football," McDaniels added. "We know he's capable of that. I think he knows that, too. I think he's looking forward to it and so are we."
Information from The Associated Press was used in this report.