Cleveland will reportedly send Nik Stauskus and Wade Baldwin to Houston in the deal.
The Kings, who gave up Shumpert, will receive guard Alec Burks from the Cavaliers in the deal. The Cavaliers acquired these two players in Sunday's trade with Portland that sent Rodney Hood to the Trail Blazers.
All three teams accomplished their objective with this multi-team trade - the Cavs traded Burks while his value was high, the Rockets acquired their 3-and-D player and the Kings added another offensive weapon as they look to continue their playoff push.
In Cleveland's fourth in-season trade, the Cavs have now gathered two first-round and six second-round picks.
Shumpert is averaging 8.9 points per game this season while shooting 38.2 percent from the field and 36.6 percent from the 3-point line.
Cleveland will bring in Knight, 27, and Chriss, 21.