The Yellows beat off competition from fellow La Liga outfit Valencia, who were hoping to lure the 30-year-old away from Estadio Gran Canaria.
The former AC Milan man's current deal with Las Palmas is set to run out at the end of this season.
"UD Las Palmas have reached a renewal agreement with Kevin-Prince Boateng for the next three seasons," the club announced on their website.
"The player will be linked to the yellow club until 2020.
"Prince, who has become the team's top scorer in La Liga with 10 goals and arrived last summer at UD Las Palmas, will hold a press conference on Thursday at the El Hornillo Sports Complex (Telde) at the end of training of the first team."
Boateng is unarguably enjoying the best season of his career so far as his 10 league goals remain his highest tally in a season.
With one game to end the campaign, the attacker, who has also played for English clubs Tottenham Hotspur and Portsmouth as well as Schalke 04, Borussia Dortmund and Hertha Berlin in Germany, has made 28 league appearances involving 25 starts.
He also has four assists to his credit.