On his first day, Mr Woldbye focused on engaging with colleagues and identifying potential improvements.
The chief executive will oversee multibillion-pound enhancements, including the introduction of advanced baggage systems in Terminals 2 and 3 and the installation of 3D security scanners.
Mr Woldbye inherits significant debt and will be tasked with resolving disputes with airlines over landing fees.
His appointment follows Heathrow's struggle to maintain profitability amid soaring debts, which currently hover around £16 billion.
Repairing strained relations with airlines, due to disagreements over landing strip charges, is also on his agenda.
There are expectations for Mr Woldbye to rejuvenate the airport's customer service and overall appeal.
Industry experts highlight that, despite high traffic, Heathrow's service quality lags behind global competitors, suggesting a refreshed approach to meet international traveller expectations may be required.
Mr Woldbye will also contemplate the future of Heathrow's proposed third runway, balancing evolving cost considerations and environmental regulations.
He said: “The UK already has a hub airport that is the envy of much of the world.
“As I spend my first days getting to know the colleagues and team Heathrow partners who make it a success, I'm looking for how we can make Heathrow even better for our customers and the British economy.
“It's humbling to have the opportunity to take on the challenge and I'm excited to get started.”