Diageo said its board felt Sir Dave had extensive chief executive experience and proven leadership skills "that is right for Diageo at this time".
"The market faces some headwinds but there are also significant opportunities," said Sir Dave.
"I look forward to working with the team to face these challenges and realise some of the opportunities in a way which creates shareholder value."
Diageo saw its operating profits decline to £3.2bn in the year to June - around 28% lower compared with the same period the year before. It said there was "clearly much more to do" in what it called a challenging year, citing "pressure on consumers".
Rising inflation has led to people tightening their spending in recent times, with consumers cutting back on drinking and eating out.
The firm has also been battling with changing drinking habits from younger people, who are opting to drink less alcohol than previous generations.
"Dave Lewis needs to put Diageo back on track quickly," said Dan Coatsworth, head of markets at AJ Bell.
"His style is to listen closely to customers and suppliers and work out what's gone wrong. The focus will be on repair work, not long-term growth."
Mr Coatsworth said the new boss earned the nicknam "Drastic Dave" while at Unilever "because of his ability to make bold decisions without simply tinkering at the edges".
"At Tesco, he walked away after saying his job to stabilise the business was done, rather than sticking around to take the business to the next level. One might suggest the same approach will apply to Diageo."
Sir Dave will replace Nik Jhangiani - Diageo's chief financial officer who has been acting as interim chief executive since Ms Crew resigned in July.
