Whitley appeared in 41 games over three separate stints with the Rays last season, going 2-1 with 2 saves and a 4.08 ERA. It was the first full season for the right-hander since undergoing Tommy John surgery in May 2015.
Tinnish was hired this week as vice president of amateur and international scouting by Alex Anthopoulos, the Braves' new general manager. The two formerly worked together with the Toronto Blue Jays.
Atlanta said Tinnish changed his mind because of family considerations, opting to remain with the Blue Jays.