Scrum-half Smith, 34, looks set for his last season in New Zealand having signed long-term with Toyota Verblitz.
Fly-half Barrett, 31, could still return home to play after 2024 following his spell with the same club.
Barrett took a sabbatical to join Japanese club Suntory Sungoliath in 2021 before returning to New Zealand.
All Blacks full-back Damian McKenzie played in Japan last season while fly-half Richie Mo'unga has signed up for the 2024 campaign.
Smith is the most-capped back in New Zealand history having played 114 times for his country, with Barrett second on 112.
Barrett said: "I'm looking forward to taking up this opportunity with Toyota alongside a good friend and long-term team-mate in Aaron."
Barrett said his agent was in "negotiation" with New Zealand Rugby, his club in New Zealand the Blues and Toyota Verblitz about his future beyond 2024.