Jerome Robinson will join the Wizards, while the Knicks will receive Moe Harkless and a 2020 first-round draft pick.
The Clippers plan to waive Thomas, league sources told ESPN's Adrian Wojnarowski.
The Knicks also will receive the right to swap first-round picks in 2021 with the Clippers (protected through the No. 4 pick), a 2021 second-round pick via Detroit and the Washington draft rights to 2018 second-round pick Issuf Sanon.
Morris, 30, will join a title hopeful in Los Angeles after improving his scoring average to a career-high 19.6 points per game this season while shooting a career-best 43.9% from 3-point range.
He will be an unrestricted free agent this offseason after signing a one-year, $15 million contract with the Knicks.
The Lakers also had talks with the Knicks about Morris, sources told ESPN's Ramona Shelburne. New York insisted on getting Kyle KuzmaandDanny Green -- to make the money work -- and future second-round picks, a haul that the Lakers found to be too much. The Lakers pulled out of talks late.
Thomas, 30, is averaging 12.2 points this season, his first with the Wizards. He is shooting a career-best 41.3% from 3-point range.
Once he is waived, the Clippers will have two open roster spots that they will look to the buyout market to fill. While Morris gives the Clippers another 3-point shooter and defender with size, the Clippers will look for a veteran playmaker, shooter, big man or defensive specialist to potentially fill those two roster spots.
Harkless, 26, is averaging 5.5 points and 4.0 rebounds this season, his first with the Clippers. He has started 38 of the 50 games he has appeared in with the Clippers.
Robinson, 22, is averaging 2.9 points, 1.4 rebounds and 1.1 assists for the Clippers this season.
Information from ESPN's Ohm Youngmisuk was used in this report.
How Marcus Morris, Isaiah Thomas fit on the Clippers
Brian Windhorst and Paul Pierce react to the Clippers acquiring Marcus Morris from the Knicks and Isaiah Thomas from the Wizards as part of a three-team trade.