Milwaukee will send its No. 71 pick in the Competitive Balance rounds of the draft to Seattle, according to Robert Murray.
The move gives the Brewers a starting catcher after Yasmani Grandal left the club in free agency to join the Chicago White Sox on a lucrative multi-year contract.
Narvaez posted a solid .813 OPS with 22 home runs across 132 games in 2019.
"Omar has established himself as one of the best offensive catchers in the game," said Brewers general manager David Stearns, according to Tom Haudricourt of the Milwaukee Journal Sentinel. "We believe his bat will give us an impactful left-handed presence in our lineup."
However, the 27-year-old is a liability behind the plate, as he finished last this past campaign in FanGraphs' defensive rating among American League catchers with 300-plus plate appearances.
Narvaez is arbitration-eligible through the 2022 season and projected to make $2.9 million in 2020.
Hill, meanwhile, is a 22-year-old righty who pitched in Single-A last season. He posted a 3.92 ERA with 109 strikeouts in 121 2/3 innings while playing for the Wisconsin Timber Rattlers of the Midwest League.
The New York Mets took Hill in the fourth round of the 2018 draft before dealing him to the Brewers in a four-player trade in January 2019. He was the No. 24-ranked prospect in Milwaukee's system, according to MLB Pipeline.