The Storm will get the Sun's second-round pick in the 2021 draft in return.
The 26-year-old averaged 5.5 points for the Storm last season and 5.3 points over her five years in the WNBA, which included a championship in 2018.
Mosqueda-Lewis won three NCAA titles at UConn before being drafted third overall by Seattle in 2015. She had a school-record 398 3-pointers for the Huskies.
''She has won championships at every level and has a reputation as a great teammate,'' Sun coach Curt Miller said. ''Our offensive philosophy revolves around spacing with players that can help spread the floor. KML is one of the outstanding shooters in our game and will provide an important spark to our offense.''
Mosqueda-Lewis said she is excited to be back in a place that served as her second home for four years.
Seattle also signed free agent guard Epiphanny Prince on Monday.
''Epiphanny's tenure in our league has been an impressive one. Her skill and versatility in the backcourt add depth to our roster,'' said Storm CEO and General Manager Alisha Valavanis. ''She is a great fit on and off the court for the Storm and we're excited to welcome her to Seattle.''
A 10-year WNBA veteran, Prince has averaged 13.2 points, 2.9 assists and 2.3 rebounds per game throughout her career, while connecting on 37.3% of her 3-point attempts.