Both players entered the NFL as draft picks of the Bears when Smith coached in Chicago. Terms of the agreements Thursday were not disclosed.
Conte was a third round draft pick in 2011 who had nine interceptions in four years with the Bears. Melton played for Chicago from 2010 to 2013 before spending last season with the Dallas Cowboys.
Melton has 20 1-2 sacks in 64 career games. He was a Pro Bowl selection in 2012, when he had six sacks for the Bears.
The Bucs signed former Dallas linebacker to a four-year, $20.5 million contract on Wednesday.