Meyer signed with the Phillies in 1951[1] and steadily rose through their farm system, winning 15 games for the 1954 Syracuse Chiefs of the Triple-A International League (IL).

[3] His most successful MLB season was his 1955 rookie campaign, when he led the National League (NL) in both saves (16) and games finished (36),[4] while fanning 97 batters in 1101⁄3 innings pitched.

[3] Meyer rebounded to post respectable seasons in both 1958 and 1959, largely in middle relief, but his career was negatively affected by his growing reputation as a drinker and late-night carouser.

Nicknamed "The Bird," he was a member — along with fellow pitchers Turk Farrell and Jim Owens — of the so-called "Dalton Gang", who received notoriety around baseball for multiple, and well-publicized, off-field incidents.

[1] For his MLB career, Meyer compiled a 24–34 record, with 21 saves and four complete games, in 202 appearances, 178 of them as a relief pitcher, with a 3.92 earned run average (ERA), and 375 strikeouts.