Roberts, who was designated for assignment by Arizona earlier in the day, is expected to join the Rays in Baltimore on Wednesday.
The corresponding move to create space for Roberts on the 25- and 40-man rosters is yet to be announced.
With Evan Longoria still recovering from a partially torn left hamstring, the Rays could view Roberts as an option at third base.
Roberts is hitting .250 with six home runs, 34 RBIs and six stolen bases this season after posting a .249 average with 19 home runs and 65 RBIs in 2011.
"I don't know if we would have won the division without what he was able to do on the field both defensively, offensively and on the basepaths," D-backs general manager Kevin Towers said of Roberts' career year in 2011. "I'm going to miss the way he played the game. He played with a lot of enthusiasm, energy and fire."
The 31-year-old Roberts has hit .250 with 35 home runs and 134 RBIs in seven seasons in the Majors.
He has made 57 of his 63 starts this season at third, posting a .957 fielding percentage. Roberts also spent time at second base and left field.
Bortnick, a 16th-round pick in the 2009 First-Year Player Draft, was hitting .253 with four home runs, 48 RBIs and 23 steals in 95 games for Double-A Montgomery this season.
Greg Luca is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.