The deal includes $20 million guaranteed, the source said.
"CHIEFS KINGDOM‼️ LET'S GET TO WORK‼️" Reid wrote Monday night on Twitter.
Reid, 25, is the likely replacement for Tyrann Mathieu, who is an unrestricted free agent. With seven interceptions, two forced fumbles, three fumble recoveries and a pair of sacks in his four seasons with the Texans, Reid has some of Mathieu's play-making ability.
The Chiefs will plug Reid into their starting lineup, where he will be joined at safety by Juan Thornhill. Kansas City may not be finished addressing the position, as their other top safety in terms of playing time last season, Daniel Sorensen, is also a free agent.
Reid, a third-round pick out of Stanford in 2018, was one of the Texans' best defensive backs in 2021, finishing the final season of his rookie deal with two interceptions, a forced fumble and four passes defended in 13 games. He was benched one game for violating team rules.
Reid's best season came in 2018, when he had three interceptions, a forced fumble, two fumble recoveries and 10 passes defended during his rookie year.
ESPN's Adam Teicher and Sarah Barshop contributed to this report.