McKenzie was earlier scheduled to join the team on July 7 but according to BCB chief executive Nizamuddin Chowdhury, he will now team up with the squad in the West Indies on July 22.
The 42-year-old, who represented South Africa in 124 matches, will take over from former Sri Lanka batsman Thilan Samaraweera.
"We are expecting his arrival on July 22," Chowdhury was quoted as saying by cricbuzz.
"We have appointed him until the next ICC World Cup. We are confident that his vast experience will help our team, and our batsmen in particular," he added.
Bangladesh will be keenly looking forward to working with him on an immediate basis especially after their recent failures in the just concluded two-match Test series against the West Indies.
The visitors lost both the Tests inside three days and it was largely due to the failure of their batsmen to apply in testing conditions.
First Published: July 18, 2018, 9:12 PM IST