Matthews is currently Pushpay's chief customer officer.
She will assume the new role on March 1.
The company announced the planned CEO transition at the annual meeting in June 2020, with a view to appointing a full-time US-based leader with strong customer affiliation.
Matthews has held senior roles within Pushpay since joining the company over four years ago.
"As the current chief customer officer, Molly has a deep understanding of Pushpay's customers' needs and the company's primary target market, the US faith sector," the company said.
Pushpay chairman Graham Shaw said Matthews had an understanding of the US faith and non-profit marketplaces and "exceptional customer knowledge".
Before joining Pushpay, Matthews was the director of K-12 Education for the Confederated Tribes of Grand Ronde in Oregon, US for seven years, where she was responsible for leading successful programmes for Native American youth and families.
She owned her own change management consulting business for more than four years where she focused on helping businesses navigate change and accelerate growth.
Matthews has been a volunteer and advocate for youth and families in various organisations for more than twenty years and has led in many capacities, including as a board member, coach, youth leader and more.
In its earnings update, Pushpay said its processing volume over the month of December was slightly higher than the company's internal forecast on November 4.
"While December donation volumes are usually significantly higher than other months partially driven by tax year-end giving in the US, the level of the increase can vary from year to year," the company said.
Pushpay also said it had allocated an initial investment of resource into developing and enhancing the customer proposition for the Catholic segment of the US faith sector.
Shares in Pushpay last traded at $1.71, up 11c from Monday's close.
