Logarzo must quarantine for seven days once she arrives in Kansas but then will join up with the team for pre-season.
The National Women's Soccer League side paid Bristol an undisclosed fee for Logarzo who still had four months left on her contract.
The 25-year-old played 12 matches for Bristol in a year-long spell and managed to score four goals.
Bristol currently sit bottom of the WSL, on just two points from 11 matches with a goal difference of negative 43.
Kansas City last had an NWSL team in 2017, but with renewed investment was welcomed back to the competition for the 2021 competition.
“She is very creative, dynamic and highly competitive,” KC coach Huw Williams said.
“She is a player who makes an immediate impact on our team both on and off the field.”
Logarazo has played in the US previously, winning the 2014 USL W-League Rookie of the Year award while at Colorado Pride where she scored eight goals and seven assists. She also played for Washington Spirit on loan in 2019.
