Hoffman is set to join the board of the UK’s second-largest building society on April 26, subject to regulatory approval.
Interim chair Peter Ayliffe is to then resume his role as deputy chair.
Coventry said Hoffman brings a wide-range of experience of financial services, including executive and non-executive positions in banking, insurance and payments services.
He is currently a director of Hastings Group and will become non-executive chairman in May 2018.
Hoffman is also on the board of Visa Europe as chairman but will step down with effect from June 30 2018.
Earlier this year, Coventry revealed its gross mortgage lending in 2017 edged down slightly to £8.6bn of mortgages in 2017, but that overall mortgage assets overall increased to £35.9bn.
The mutual said it expects competition in the mortgage market to maintain pressure on margins this year.