He replaces David Cutter, group chief executive of Skipton Building Society, who has held the post for the past two and a half years.
At the same time, Chris Pilling, chief executive of Yorkshire Building Society has been elected as deputy chairman.
Jenkins said: “We have had a lot of wins over the past months and the sector continues to provide competition and choice to consumers looking for an alternative on the high street.
“One of the reasons for this is because of the excellent story we have about customer service and satisfaction, product development and innovation. This is good news, but our primary objective has always been to meet - and surpass - the ever-evolving needs of our members. If we continue to do this, then we are on to a winner.
“My focus this year is to continue the admirable work that David Cutter has done to champion the sector – locally, nationally and in Europe.
“In terms of niche and non-standard lending, financial education, talent development and the customer experience we are strong.
“What I need to do now is to ensure that this work can continue. There is always more we can do, but we also need good regulatory and parliamentary support so that we are fully equipped to tackle the challenges ahead.”
