Davie replaces John Smith, who steps down as Worldwide boss after guiding the division through eight years of record growth to become a billion pound business.
He told staff today that he is leaving the BBC to "pursue new opportunities in the commercial sector".
"It has been a huge privilege to lead this powerful business, owned by the BBC that does so much to supplement the licence fee income and takes the BBC brand to audiences around the world," said Smith.
"I am extremely proud of what we have achieved over the last eight years but I am excited to be moving on to new opportunities in the commercial world as our revenue and profits reach record highs."
BBC director general George Entwistle has picked Davie to succeed Smith, and he will have a tough act to follow when he starts at Worldwide on December 1.
Smith, who was previously the BBC's chief operating officer, has helped Worldwide to become the planet's largest owner of TV channels and the biggest distributor of TV content outside of the US giants.
The BBC's international channels now attract more than 360m subscribers around the world; BBC.com is profitable; and the subscription-based global BBC iPlayer is available in 16 countries.
"I want to thank John for his enormous contribution to the success of BBC Worldwide in recent years," said Entwistle.
"He has turned the company into a truly global phenomenon delivering a fantastic financial injection into the BBC every year. He leaves the company ideally set up for the future challenges it faces in a digital world."
"Building on John's success Tim will now take the BBC's commercial arm into the next chapter of its development. I am delighted he will be joining the team at this crucial time."
Davie described BBC Worldwide as an "outstanding business that plays a unique role in building the BBC's global reputation".
He added: "It is an honour to be asked to lead it. John's legacy is a company with a strong performance record, leadership in digital and rising international creative exports.
"I look forward to leading BBC Worldwide through its next phase of growth, delivering further dividends to the BBC and championing great British content around the world."
Davie has been the BBC's Director of Audio & Music since 2008, and was previously the director of BBC Marketing. Prior to joining the corporation, he was a senior executive at PepsiCo Europe.
The BBC has not yet confirmed who will replace Davie as its new music director.