Penn joined the telco in 2012 as chief financial officer, and was promoted to the top job in May 2015.
He led the company through a tumultuous time of restructuring and staffing cuts, a strategy it labelled "T22", plus the COVID-19 pandemic.
While Penn himself did not comment, chair Mullen paid tribute to the outgoing chief.
"Delivery of the T22 strategy has seen Telstra return to underlying growth, achieve significant customer experience improvements, reduce costs by over $2.5 billion and reach high performing employee engagement levels with over 17,000 people now working in agile teams across Telstra," he said.
"There is no doubt the strategy has delivered beyond expectations and has laid the foundations for Telstra's recently announced T25 strategy and a renewed focus on growth and innovation."
What's new Telstra chief Vicki Brady about?
Brady came to Telstra in 2016 and held the positions of consumer group managing director, sales and service group managing director and consumer and small business group executive. She then became CFO in July 2019.
With the CEO role, she lands a fixed annual salary of $2.39 million plus incentive payments that could end up 200% to 300% of that amount.
Mullen credited Penn with developing a strong enough leadership team around him that an internal candidate like Brady could step in as chief.
"She has made a significant contribution to Telstra including her work in developing our new go to market plans as part of the T22 strategy," he said.
"She has played a key leadership role in the development of Telstra's T25 strategy and is well placed to lead the company through its next phase."
Before Telstra, Brady worked for rival Optus, its parent company Singapore Telecommunications Limited (SGX: Z74) and KPMG.
She holds a bachelor of commerce from the Australian National University and a master of science in management from the Stanford University Graduate School of Business.
Brady is a member of Chartered Accountants ANZ and is a graduate of the Australian Institute of Company Directors.
Telstra shares have lost 6.87% for the year so far, but are up 14.6% over the past 12 months.
The company currently pays out a dividend yield of 2.84%, with 9 of 14 analysts surveyed on CMC Markets rating the stock as a buy.
The stock closed Tuesday at $3.93.