Arrangements are being made to send a plane to Bardai to evacuate Godbold to N'Djamena, Chad's capital, the group said.
Team said: "From there he will travel to the United States via Europe for reunion with family and colleagues, debriefings and medical checks."
The evangelical group said that Godbold was "ultimately released following extensive negotiations between his captors and Team."
"Team emphasises that Godbold's release was unconditional and that no ransom was paid and no concessions of any type were made to secure his release."
Godbold, 49, was held by Chad's Movement for Democracy and Justice in Chad (MDJT) on suspicion of being a spy for the Chadian government.
MDJT was formed in Chad's mountainous north in the late 1990s but it has been eclipsed in recent years by eastern rebels battling Idriss Deby, the Chadian president, from bases near the border with Sudan's Darfur region.
Mahamat Hissene, Chad's communications minister, said he could not confirm Godbold's release but added that "there will be a meeting about this matter tomorrow".
He said the meeting would be at the interior ministry, but declined to give any details.
At the time of his seizure, Godbold was working on a humanitarian assistance project drilling water wells in the Zoumri region, funded by the US defence department.
The MDJT had suggested on several previous occasions that he was about to be freed, but to no avail.
In January the MDJT said its inquiries showed that Godbold was not working for the Chadian government as it had originally suspected.