The Broncos later confirmed the trade while announcing their cuts.
Smith's departure bookends a frustrating chapter with the Broncos. Denver acquired Smith with the 37th overall pick in the 2009 NFL Draft, swapping its first-round pick in the 2010 NFL Draft for the Seattle Seahawks' 2009 second-rounder -- a move that generated a fair share of second-guessing in the media.
"It speaks volumes that coach McDaniels and the Broncos staff thought I was a first-round talent so they gave up a first-round pick for me," Smith after being drafted. "Hopefully, it won't be so controversial after this season."
Smith, from Wake Forest, played in 15 games in his rookie year, recording just 14 tackles.
Gronkowski, 25, was drafted by the Lions in the seventh round last year out of Maryland. He appeared in two games last season, catching one pass for 4 yards.
The Associated Press contributed to this report.