The suspensions begin during the 2017-18 regular season.
Pacers president of basketball operations Kevin Pritchard was disappointed in Ellis' suspension.
"Monta's suspension is a very serious matter to our franchise and it will be dealt with accordingly," Pritchard said in a statement.
Ellis, 31, averaged 8.5 points last season, his lowest output since his rookie season (2005-06).
Bullock, 26, averaged 4.5 points in 31 games for Detroit last season.