Joseph nominally led Haiti following the assassination of President Jovenel Moise earlier in July. Henry was appointed prime minister by Moise just a few days before he was killed.
Joseph will become the new foreign minister, AFP reported, citing sources.
The new government will be formed on Tuesday, it won't have a president and will deal with organising fresh elections, the agency added, quoting a government official.
Moise was shot dead at his residence on July 7. His wife, Martine, was wounded and airlifted to a US hospital. The police said that they had identified 28 suspects, with at least 23 of them having been detained. Most of the suspects are Colombian citizens.