The video showed Nelms stealing a pair of $300 earrings that homeowner Daniel Dillon bought for his wife.
Angered by the crime, Dillon posted the video on social media and it was shared thousands of times.
"People on the internet love stupidity and this guy is as stupid as they come. There's five cameras on the front (of the house) and he didn't pay any attention," Dillon said.
Nelms explained his side of the story to RTV6 reporter Chris Proffitt.
"I seen the FedEx truck and seen him turn around and where he dropped the package off. Went up there and that's what it was. I wasn't thinking," Nelms said. "I knew what I was doing. I didn't kill anybody. I didn't hurt anybody."
Nelms said he is homeless after he was kicked out of his parents’ house following his release from jail. He was arrested after a probation violation in Florida for carrying a handgun.
He said he has been on his own since he was 16 and he claimed he stole the earrings so he could buy food.
"The reality of it is, you're homeless, but I'm not willing to live under a bridge or in a shelter. So if it means I have to steal something where nobody gets hurt. I'm not condoning what I did. Stealing's wrong. That's why I'm here. I've paid my debt to society for every crime I've committed," Nelms said.
Nelms has an extensive criminal record. Police said he has been involved in burglaries, thefts and various other crimes.