ESPN's Josina Anderson also reported Ford would receive a five-year deal for $87.5 million once the trade becomes official.
Ford, who was selected out of Auburn with the 23rd overall pick in 2014, is coming off his best season.
After missing several games with injuries throughout the course of his career, Ford played all 16 weeks for the first time since his rookie season.
Ford, 28, was amenable to playing 2019 on the franchise tag, but Kansas City is shifting away from the 3-4 defensive scheme it used under former defensive coordinator Bob Sutton, who was sacked at the end of the season after leading the NFL's 31st-ranked defense. Their leading edge rusher was Cassius Marsh, who recorded 5.5 sacks in 2018.
Kansas City's defensive scheme change from a 3-4 to a 4-3 was a key reason why the team shopped Ford. The 49ers will send their second-round pick in 2020 to the Chiefs in exchange for the pass rusher.
The 49ers were reportedly one of two teams interested in Ford, according to an earlier report by Rapoport. Ford has racked up double-digit sacks in two of his past three seasons.
The deal clears $15 million in salary-cap space for the Chiefs.
There's a bit of an issue contractually because the Chiefs placed a franchise tag on Ford.
That has the potential to be a premier pass rushing foursome which could be swing the team's historic takeaway numbers in the other direction.
For the Chiefs, the second round pick in 2020 won't do anything to help them rebuild a defense that also lost Justin Houston.
The 49ers finished 2018 tied for 22nd in the National Football League in sacks with 37, but aside from Buckner, they did not have another player with more than 5.5 sacks.