During the 1976 Major League Baseball expansion draft, Meyer was selected by the Seattle Mariners, who chose him ninth overall. On June 9, 1977, in a game against the Minnesota Twins, Meyer hit two home runs. In his first season with the Mariners, Meyer batted .273 with 75 runs scored, 159 hits, 24 doubles, four triples, 22 home runs, 90 RBIs, and 11 stolen bases in 159 games played. He led the American League with 159 defensive games at first base. During the Mariners inaugural season, he led the team in hits and RBIs. Meyer also set multiple career highs in 1977 that would stand until the end of his professional tenure in games played, plate appearances (639), at bats (582), runs scored, hits, home runs, RBIs, walks (43), strikeouts (51), on-base percentage (.320), and total bases (257).