The Scotland international is Spurs' first acquisition of the summer after staving off relegation from the Premier League.
Spurs head coach Roberto De Zerbi said: "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.
"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.
"I can't wait to start working with him and seeing the positive impact he will have on everyone around him."
Tottenham tried to sign Robertson in January, but Liverpool blocked a move due to being unable to recall Kostas Tsimikas from his loan at Roma.
Reports emerged that Juventus made a late enquiry about the 32-year-old, but he elected to stick with his original plan of joining Spurs.
Robertson enjoyed a successful nine years in Merseyside, which brought a haul of trophies, including two Premier Leagues and the Champions League across 378 appearances.
He has 93 caps for Scotland and is set to lead the Tartan Army this month at their first World Cup since 1998.