Players have 72 hours to report to their new club once they are traded.
"I told him we're not in a roster crunch, so whatever works best for him," interim general manager Jerry Dipoto said.
Once Church reports, the D-backs will need to clear a spot on the roster for him, with the decision likely to be between infielders Augie Ojeda and Tony Abreu.
The reason the team elected to send down outfielder Cole Gillespie when infielder Bobby Crosby joined the team Sunday was because Ojeda and Abreu are both switch-hitters, and the team wanted to swap out right-handed bats with Crosby and Gillespie to keep flexibility on the bench.
"Cole is going to go down and play every day for the last month and probably deserve to come back in September," interim manager Kirk Gibson said.