The 24-year-old has signed a five-year contract after Spurs agreed to match an undisclosed buyout fee set out in his most recent Burnley contract.
Former Manchester City trainee Trippier has spent the past four seasons at Turf Moor, the first of them on loan, but departs following the club’s relegation to the Championship.
He said: “When I first heard that the club was interested I didn’t have to think twice. It’s such a big club and now I just can’t wait to get started and show everyone what I can do.
“Whenever I get a chance, I want to do well for the other players, the staff and, of course, the fans. I’ll take every opportunity I get with both hands and hopefully play my part for everyone at the club.”
Trippier, who is Spurs’ second summer recruit following the arrival of Kevin Wimmer, will compete with England’s Kyle Walker for the right-back role at White Hart Lane.