Joseph was waived by the Dolphins on Tuesday.
Joseph is inactive for Sunday's game against the Giants.
Dallas traded Joseph to Miami in exchange for Noah Igbinoghene on Tuesday, Josina Anderson of CBS Sports reports.
Joseph (back) participated in Dallas' practice Saturday, the team's official site reports.
Joseph exited practice Wednesday with a back injury, Clarence E. Hill Jr. of the Fort Worth Star-Telegram reports.
Joseph is expected to start opposite Trevon Diggs moving forward, Todd Archer of ESPN.com reports.
Joseph (illness) was not listed on the Cowboys' injury report Wednesday, Jon Machota of The Athletic reports.
Joseph (illness) is inactive Thursday against the Giants, Todd Archer of ESPN.com reports.
Joseph exited Sunday's game against the Vikings due to an illness, Michael Gehlken of The Dallas Morning News reports.
Joseph (concussion) isn't listed on Wednesday's injury report, Jon Machota of The Athletic reports.