Broncos boss John Elway announced the deal Wednesday on Twitter, saying: "Our team has a lot of depth in the secondary and this is an opportunity for us to add a quality fullback to our roster."
The only other fullback in Denver is Austin Sylvester, who hasn't played in the NFL.
Gronkowski has played in 21 games with Dallas (2010) and Indianapolis (2011). He has two brothers in the NFL: Rob, an All-Pro tight end in New England, and Dan, a tight end in Cleveland who played for Denver in 2010.
Vaughn played in 22 games with the Broncos, making 22 tackles and returning an interception for a TD.