Johnson, 36, will clear waivers on Monday afternoon and be eligible to sign immediately thereafter.
Johnson is the second player to commit to signing with the Rockets out of the buyout market. Forward Brandan Wright, who officially was waived the Memphis Grizzlies on Saturday, will sign with the Rockets upon clearing waivers, league sources told ESPN's Chris Haynes.
And, along with Gerald Green, the Rockets will now have acquired three veteran contributors without surrendering any assets. Green, who is averaging 13.9 points per game for the Rockets, was unemployed for more than two months this season.
The Rockets on Friday re-signed guard Bobby Brown for the rest of the season but will now waive him to clear a roster spot for Johnson, league sources told ESPN.
Johnson had played a minor role off the bench for the Jazz this season, averaging 7.3 points and 3.3 rebounds. According to ESPN Stats & Information, he is 39 3-pointers shy of becoming the ninth player in NBA history with 2,000.
ESPN's Tim MacMahon contributed to this report.