The forward, who scored 33 goals in 43 Liga F games for Madrid, has agreed a four-year deal with the American club, with the option of a further year.
Bay FC will make their National Women’s Soccer League debut this year.
Kundananji, 23, becomes the first African player, male or female, to break a world transfer record.
England midfielder Keira Walsh was previously the most expensive women’s player following her £400,000 switch from Manchester City to Barcelona in 2022.
That could be surpassed by Chelsea’s deal to sign Colombia striker Mayra Ramirez from Levante for an initial £384,000, with add-ons potentially taking it up to £426,600.
However, that fee will now be a distant second following the landmark deal to take Kundananji from Spain to San Jose, where Bay will play their home games.
“People in Zambia will be surprised but they will be so happy,” Kundananji told BBC Sport Africa.
“I want to give the [Bay FC] fans what they want – to enjoy the games, to enjoy seeing me playing and scoring.”
Bay will pay an initial $785,000 for Kundananji, with a further $75,000 in add-ons.
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‘Has composure’
“We are delighted to add Racheal to our group,” Bay FC general manager Lucy Rushton said in a press release from the club. “She is a tremendous talent with dynamic attacking qualities and an incredible physical profile who has produced for both club and country.
“Racheal has a composure in-front of goal and a natural ability to score with different types of finishes and from various locations.
“We believe she will continue to grow and develop at our club, showcasing her skillset and adding to the array of exciting talent we have here.”
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Kundananji began her career with Zambian side Indeni Roses before moving to BIIK Kazygurt in Kazakhstan in 2019, where she first played in the Women’s Champions League.
Two years later, she joined Spanish top-flight side Eibar and eight league goals in her only season with the Basque club earned the pacey forward a move to Madrid.
She scored 25 goals in 29 league games to help Madrid CFF to a fifth-placed finish, the best in their history, last season and has added another eight in 14 league matches this campaign.
Kundananji also played – and scored – at the 2023 Women’s World Cup and has 10 goals in 18 games for Zambia.
The latest big-money move adds to the record spending in the women’s game with world governing body Fifa reporting that transfer fees totalled $2.1m in January, a 165.5% increase on January 2023.
That is despite the number of international transfers rising by just 0.3% from 12 months ago.
Kundananji joins Nigeria striker Asisat Oshoala and former Arsenal defender Jen Beattie at Bay FC after both players signed deals with the club earlier this month.