"It's a done deal," said Chief Coach Dick Vermeil, who coached Green with the Rams. "They give us Trent Green and their fifth-round choice and don't re-sign Tony Horne."
The Chiefs had been talking with the Rams for more than a month. They signed Horne, a wide receiver-kick returner, this week to an offer sheet that the Rams initially said they would match.
"This deal probably could have been done a long time ago if we had been absolutely sure of Trent Green's health," Vermeil said.
The 29-year-old Green is rehabbing a knee injury.
Earlier Friday, the Chiefs signed quarterback Bubby Brister to a one-year deal.
Going for quality over quantity in his final draft as Green Bay general manager, Ron Wolf swapped five of the Packers' draft picks for three of San Francisco's.
In the second round, the Packers exchanged the 47th overall pick for San Francisco's 41st overall selection. Green Bay also moved up in the third round, sending the 71st overall pick to the 49ers for the 80th and 82nd picks. The Packers also got a fourth-rounder by trading a sixth-round pick (179th) and a seventh-rounder (222nd).