The left-handed-hitting Narvaez, 27, had a career season for the Mariners in 2019, hitting .278 with 22 home runs and 55 RBIs in 132 games.
"Omar has established himself as one of the best offensive catchers in the game," Brewers general manager David Stearns said in a statement. "We believe his bat will give us an impactful left-handed presence in our lineup."
Narvaez appeared in 98 games at catcher with a .994 fielding percentage, and he threw out 13 of 71 base stealers (18%).
Hill, a 22-year-old right-hander, was 7-9 with a 3.92 ERA in 26 games for Class A Wisconsin of the Brewers' system last year.
The news of the trade was first reported by The Athletic.
The Mariners acquired Narvaez from the White Sox on Nov. 30, 2018, in exchange for reliever Alex Colome, who took over as Chicago's closer last season.
The Brewers also have catcher Manny Pina, who hits right-handed, under contract for the 2020 season. Pina isn't an offensive threat, hitting just .228 with 7 homers and 25 RBIs in 76 games last season, but he threw out 25% of attempted base stealers (7 of 28) and had a .993 fielding percentage.
The Mariners will likely hand the starting catching duties in 2020 to Tom Murphy. The 28-year-old Murphy had a strong 2019 season at the plate, hitting .273 with 18 home runs and 40 RBIs in 75 games. He appeared in 67 of those games at catcher and threw out 13 of 33 attempted base stealers (39%) and had a .994 fielding percentage.
Murphy likely will be backed up by Austin Nola going into the season. Seattle also has top catching prospect Cal Raleigh.
"We were fortunate in 2019 to develop really good depth at the catcher spot, with Omar, Tom Murphy and Austin Nola at the big league level, and Cal Raleigh rising quickly in our minor league system,'' Seattle general manager Jerry Dipoto said. "That depth allowed us to make a move today that we think will pay long-term dividends to us, while not impacting us in the short term.''
ESPN's Jeff Passan and The Associated Press contributed to this report.