The 20-year-old has joined the Czech First League club on a "long-term" deal ahead of next year's World Cup after a troubled two-year stint in the Premier League.
Kuol had joined the Magpies in 2023 after playing in the 2022 World Cup, but struggled for game time after that.
The former Central Coast Mariners winger was first loaned to Scottish side Hearts before struggling to break into a Volendam side that was relegated to the Dutch second division in 2024.
Kuol moves to Sparta Prague to link up with former Newcastle U21 coach Diarmuid O'Carroll, who made his way to the Czech club as an assistant earlier in June.
The winger had impressed in Newcastle's reserve team, finishing with five goals and four assists in 11 matches during the Premier League 2 season.
Sparta Prague interim sporting director Tomas Sivok said the club saw "great potential for growth" in Kuol.
"Garang is a talented winger who, despite his age, already brings plenty of experience," Sivok said in a club statement.
"We were impressed by his pace, his ability to operate on both sides of the pitch, and above all, his courage in one-on-one situations.
"We see great potential for growth in him. At the same time, it's important that he is given enough time to adapt."
With less than a year until the World Cup in June, Kuol could convince Socceroos coach Tony Popovic for a recall.
Kuol hasn't played for the Socceroos since making his fifth national team appearance in 2023.
His move to Sparta Prague comes after Popovic handed fellow youngster Nestory Irankunda his first call-up in 10 months for Australia's friendlies against New Zealand in Canberra next Friday and Auckland three days later.
Irankunda recently moved to English Championship side Watford from Bayern Munich.
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