The deal is worth $68 million, according to ESPN and multiple reports.
The extension will begin in 2020 and run through 2023.
Mikolas, 30, is entering the second year of a two-year, $15.5 million deal.
Mikolas emerged as one of the National League's best pitchers last season after spending the previous three seasons playing in Japan. The right-hander went 18-4 with a 2.83 ERA in 32 starts last season, tying for the league lead in wins.
Mikolas, a first-time All-Star last year, is 22-10 with a 3.61 ERA in parts of four seasons with the Cardinals, Rangers and Padres.