Mallinder, 25, the son of Scottish Rugby Union's performance director Jim Mallinder, made 253 appearances and scored 83 points after coming through the ranks at Franklin's Gardens.
After making his debut in 2013, he played full-back, fly-half and centre for the club but is keen to settle into the fly-half role in Japan.
Mallinder, a member of the England squad that toured Argentina in 2017, had seen his career stand still under Chris Boyd at Saints after several injury problems.
But Saints do have an option for him to return to the club in two years' time, ahead of the 2023–24 season as part of the agreement of letting him leave.
The Green Rockets, based in Abiko, was home last season for Saracens full-back Alex Goode, who joined after the former Premiership champions were relegated.
Rockets head coach John Kirwan is looking for another fly-half after Goode returned to north London to help Saracens win promotion back to the top flight.
The Green Rockets have also been holding talks with Stormers' target, Curwin Bosch, despite him being under contract to the Sharks until 2023.
The Sharks, who have been boosted by investment from MVM Holdings, are determined to hang on to the Springbok until the end of his contract at least.
Meanwhile, Leicester Tigers have made Tongan back Hosea Saumaki their ninth signing ahead of the 2021-22 season.
BY NEIL FISSLER
