The Saints had until Tuesday to match the offer sheet. He got the low tender offer, so there would have been be no draft pick compensation if the Saints didn't match the offer.
Bush is a former undrafted free agent from South Carolina State who has also played for the Denver Broncos.
He signed with the Falcons in 2010 out of college.
Last season, he played in 13 games with six starts for the Saints and had a career-high 42 tackles
Follow me on Twitter: @RavensInsider
Aaron Wilson covers the Ravens for The Baltimore Sun