Paterson will join the mutual in May and take over the role in July subject to regulatory approval.
He was most recently director of banking and marketing at Secure Trust Bank, a role he has held for around six years.
Prior to that he worked at Coventry Building Society for around seven years across several senior roles across product and proposition development as well as strategy and customer insight.
Dudley Building Society said during the recruitment process, Paterson “demonstrated a clear understanding of all of the qualities required of a chief executive and a desire to build on our position”.
Wood has been chief executive of the mutual for nearly a decade, and before that was chief executive at OneSavings Bank for around a year.
Prior to that he was director at C2 Partnership and before that worked at Nationwide for over two decades in various senior roles.
The mutual said he had signaled to the board two years ago he planned to retire in 2022.
Wood said: “It’s been an enormous privilege and we’ve come a long way in positioning Dudley as a really credible regional society.”
Dudley’s chair Peter Hubbard said: “The board is grateful to Jeremy for what has been achieved over the last 10 years in particular helping us to reach more members than ever, and in later years ensuring we have been able to provide support to members during the pandemic.
“We remain excited about the future and in particular doing the best for our members. We are conﬁdent that James will continue to help us drive the society forward.”