The deal can't become official until July 10, after next season's salary cap has been set. The Rockets can give him a four-year deal worth about $88 million, a year less and far below the $118 million the Lakers could have offered.
The Lakers acquired Howard last August from Orlando as part of a four-way trade that also included Philadelphia and Denver.
He averaged 17.1 points and 12.4 rebounds in 76 games, good numbers but far from his usual dominant play in eight seasons with the Magic as he played his way back into shape following back surgery.
He wasn't a natural fit in D'Antoni's system, had what appeared at times to be a strained relationship with Bryant and acknowledged not having fun at times.
Bryant apparently won't miss him. Though he took part in the Lakers' meeting with Howard on Tuesday, the five-time champion posted a photo on Instagram of himself and Pau Gasol, the Lakers' remaining big man, shortly after Howard's decision.
Howard's awkward departure is right in line with the confusion that's followed him over the last few years.
The No. 1 pick in the 2004 draft was one of the NBA's most popular and likable players, an Olympic gold medalist who led the Magic to the 2009 NBA Finals — where they lost to Bryant and the Lakers.
But he decided a couple of years later that he wanted out of Orlando, and the Magic eventually gave his agent permission to negotiate with the Nets, Mavericks and Lakers about arranging a trade.
Yet Howard would later agree to not opt for free agency, remaining with the Magic for the 2011-12 season. Howard's season ended prematurely when he needed back surgery, and Orlando finally dealt him to Los Angeles.
The Lakers' season was a disappointment, with Bryant, Gasol and Steve Nash all missing time with injuries. They never developed any chemistry, getting swept in the first round of the playoffs by San Antonio.
The Rockets believe he'll find that chemistry in Houston.
"We have good teammates. They're young. They're guys who are great not only on the floor but off. He's going to get along great with our team," Morey said in an interview with Comcast SportsNet Houston.