The New Zealander has agreed a two-year deal and will move from the Championship club this summer.
Leinster’s move for Gopperth comes after current No 10 Jonathan Sexton secured a lucrative switch to French club Racing Metro, starting next season.
Gopperth, 29, has scored more than 700 points for Newcastle. He played Super Rugby with the Blues and Hurricanes in New Zealand before heading to England.
Leinster head coach Joe Schmidt said: “We are delighted that Jimmy has put pen to paper on a deal. We believe that he will be an excellent foil for Ian Madigan, bringing added depth and experience to the out-half position when he joins this summer.
“Even though Newcastle have struggled in recent years, he has been a hugely consistent performer during his time in England, where he won back-to-back Premiership Golden Boot awards.”
Newcastle Falcons director of rugby Dean Richards added: “Jimmy has been a fantastic servant for the club, and I would like to wish him all the very best for the future.
“By moving to Leinster, Jimmy will get the opportunity to play Heineken Cup rugby next season.”