The 24-Test veteran, Grand Slam winner in 2018, and a member of the Ireland team at the 2019 Rugby World Cup was part of the fallout when the Wasps club went into administration earlier this year. He then joined Munster, for who he had earlier played 197 games, on a three-month contract for the remainder of the 2022 season.
Ryan most recently was part of the Barbarians side who beat the All Blacks XV in London last month. He and his family will move to New Zealand in February before the Super Rugby Pacific season.
"It's a very exciting challenge that myself and my family are very much looking forward to. The Chiefs are a top-class team, and I look forward to adding what I can to their vision and goals for the season ahead," he said.
Chiefs coach Clayton McMillan said it was a blow to lose Ta'avao as he was an influential leader and prominent personality.
"Finding a replacement with relative experience has not been easy, and we are delighted to have landed with John.
"We have players who have opposed and played alongside him on the recent All Blacks XV tour and Barbarians fixtures.
"They strongly advocated his ability and character. His history at Munster and Ireland speaks volumes of his ability and durability, and we look forward to welcoming John and his family into the Chiefs' whānau."
Chiefs chief executive Simon Graafhuis said having Ryan's experience available was exciting.
"We usually lose the talent to the northern hemisphere, particularly experienced tight forwards, so it is nice to get one back this way.
"It was important to bring some experience into the squad. Tighthead is such an important role, and is a core part of setting up a decent platform for the team to attack from. We look forward to welcoming John, and we wish Angus well with his recovery."