He initially posted his thoughts on Twitter, and then explained his thought process in an interview Tuesday with "The Herd With Colin Cowherd" on ESPN Radio.
"You can post this where ever.. Denver broncos will win the Super Bowl 2013 #4UJEREMIAH #IGUARANTEEIT58 if you are with us Retweet," he tweeted earlier Tuesday.
That tweet came after another tweet where he announced that his 6-year-old cousin, Jeremiah Clark-Martinez, had emerged from a coma, after a car accident in Texas that also injured Clark-Martinez's mother and 8-year-old brother.
"This is why we win the Super Bowl 2013. My little cousin Jeremiah came out of a coma frm a car wreck In west Tx I [love] U," he wrote.
In the interview with ESPN Radio, he went into more detail about his cousin's recovery, explaining his boast wasn't about him "being cocky" but that his cousin had motivated him to make the bold guarantee.
"I was motivated by my younger cousin ... he got in a wreck about a week ago and he just came out of a coma a couple of days ago," he said. "His first couple of words was, they asked him a couple of questions and, of all the stuff to remember, he remembered that his cousin played for the Denver Broncos and his name was Von Miller."
That was enough to fire Miller up for the upcoming season.
"It just moved me and I'm motivated and I'm going to work extremely hard. Not like I haven't done it before, but this year it's just a little bit extra for me and I'm extremely motivated," he said.
When he was asked how Peyton Manning will react to his guarantee, Miller said he doesn't think his quarterback will mind.
"I think he already has a personal guarantee with himself," he said. "I'm not speaking for anybody else, I'm speaking for me and the work I'm going to do and the work I'm putting in this year, but I bet I have some guys in the locker room that's willing to work with me and take the path I'm willing to take."
The Broncos entered the playoffs last year as the No. 1 seed in the AFC, buoyed by Manning's Comeback Player of the Year season, but lost to the eventual Super Bowl champion Baltimore Ravens in overtime after allowing a deflating 70-yard tying touchdown reception by Jacoby Jones with 31 seconds remaining in regulation.
In a later interview with The Associated Press, Miller said he has faith that safety Rahim Moore, who allowed Jones to haul in Joe Flacco's 70-yard touchdown heave in the final minute of regulation, will bounce back along with the rest of the Broncos.
"In that game, Rahim made a few key tackles. He was making plays. He was all over the place. That play was just a football folly and the ball was able to get over him and they were able to score a touchdown," Miller said. "On that play, I don't blame Rahim. I mean, I blame me and Elvis (Dumervil). There was 40 seconds left in the game, they've got 70 yards to go, we know they're going to pass the ball. That's why they bring me and Elvis in ... to close it out and capitalize on that.
"So, I mean, I'm sure Rahim took it hard. I took it hard, too. Me and Elvis took it hard equally. We're going to use all that, we're going to mash it all together and we're going to be motivated."
Miller set a Broncos single-season record last year with 18.5 sacks.
Information from The Associated Press was used in this report.