"I feel like I can be myself a little more for sure," Welker told the website in the interview, which was conducted last week.
He said the Broncos haven't told him to avoid talking about certain subjects, unlike in New England, where players' comments may sometimes come under the scrutiny of coach Bill Belichick.
"All they told me was 'Just be yourself,'" he told the website.
His former quarterback, Tom Brady, took the high road when he addressed Welker's departure in a radio interview last month, but Welker told Yahoo! that the Patriots star was upset with New England's decision to let the receiver sign with another team.
"He was upset about it, and part of me was a little upset about it too. But things happen for a reason, and I'm excited about the opportunities here and the type of team we have and things that we can do," he told the website.
He said the move to the Broncos and quarterback Peyton Manning was "by design."
"There weren't too many quarterbacks that I would've gone out there and played with," he told Yahoo!
Welker also told the website that he'll use the Patriots' decision to let him test free agency and ultimately replace him with Danny Amendola as motivation this season.
"Wherever you can pull any sort of motivation that you need to use to go out there and play the way you need to play, I say use it," he told Yahoo!
Welker and the Broncos are scheduled to face the Patriots in Week 12 at Foxborough.