The 32-year-old will officially join Spurs on July 1 after leaving Liverpool at the end of his contract, bringing an end to a glittering nine-year spell at Anfield during which he established himself as one of the Premier League's most accomplished full-backs.
Robertson arrives as Tottenham begin reshaping a squad that only secured top-flight survival on the final day of last season. De Zerbi's side finished just two points above the relegation zone after defeating Everton, and the Italian has wasted little time in targeting experienced players capable of helping steer the club away from another battle at the bottom.
"Andy is someone I've admired for a number of years and he will bring outstanding technical qualities, experience, leadership and mentality to our team," De Zerbi said.
"He is a proven winner at the highest level over a long period and is someone who can be a big player for us, both on and off the pitch."
Tottenham's interest in Robertson is not new. The north London club attempted to sign him during the January transfer window when Thomas Frank was still in charge. A deal was initially agreed, but Liverpool ultimately withdrew after being unable to recall Kostas Tsimikas from his loan spell at Roma, leaving them short of defensive cover.
There was also late interest from Serie A giants Juventus before Robertson opted to move to north London.
Spurs sporting director Johan Lange highlighted the qualities that made Robertson a priority target.
"His quality, character and leadership have been evident throughout a career in which he has regularly competed for – and won – major honours," Lange said.
"Andy's professionalism and commitment will also be invaluable to the development of our squad, and he shares our ambition and determination to bring success back to the club."
Robertson leaves Liverpool having made 378 appearances since arriving from Hull City in 2017. During his time at Anfield he collected two Premier League titles, a Champions League crown, an FA Cup, two League Cups and a Club World Cup, while also contributing 69 assists.
The defender will now look to add to his 92 international caps when he captains Scotland at the upcoming World Cup, the nation's first appearance at the tournament since 1998.