The two sides agreed to a one-year deal worth $11.7 million, according to multiple reports.
"I'm happy that we were able to come to an agreement and avoid arbitration," Correa said in a statement. "Arbitration is not a good process."
Correa had been seeking $12.5 million in 2021, while the Astros had offered $9.75 million.
The 26-year-old hit .264 with five home runs in 58 games last season but saw his numbers improve to .362 with six homers and 17 RBIs in 13 playoff games. Houston lost to the Tampa Bay Rays in Game 7 of the ALCS.
Correa led major league shortstops with a .995 fielding percentage, making just one error.
Correa made $2,962,963 in 2020, a proration of his original $8 million salary, as a result of the COVID-19 pandemic.
MLB Network first reported financial details of the settlement.
Information from The Associated Press was used in this report.