The deal also includes $2 million in performance bonuses, according to the reports.
Gonzalez also spent the final month of last season with the Brewers, who acquired the two-time All-Star in an Aug. 31 trade with the Washington Nationals.
Gonzalez signed a minor league deal with the Yankees earlier this season but was released by New York on Monday after spending a month in the minors.
Gonzalez, 33, returns to a Milwaukee team that enters play Wednesday with a 5.34 team ERA, the worst in the National League. The Brewers are also without injured starters Freddy Peralta and Jimmy Nelson.
Gonzalez went 3-0 with a 2.13 ERA in five starts with the Brewers last season. He was 10-11 overall with a 4.21 ERA in 32 starts with Milwaukee and Washington.
ESPN's Jeff Passan contributed to this report.