In exchange, the Cardinals are receiving outfielder prospects Alexander Frias (Single-A) and Josiah Ragsdale (Double-A).
May, 28, is coming off a one-hit, five-inning shutout against the Chicago Cubs, only allowing one run over his last 12 innings pitched.
The 2020 World Series champion has a 4.38 ERA this season with 106 strikeouts and 35 walks through 109 innings this season.
Romero, 29, has a 3.35 ERA through 44 games this season. The veteran reliever has finished each of the last three seasons with an ERA below 3.70, including a career-best 2.07 in 2025.
May spent the first five-and-a-half seasons of his career with the Los Angeles Dodgers before the team traded him to the Boston Red Sox last season. The vet tossed his first complete-game shutout earlier this season in a win over the San Diego Padres.
He needs just 18 more strikeouts to set a new single-season high.
Cardinals' return
Frias, 18, is hitting .342 with a .980 OPS, eight home runs, 62 RBI, and 19 stolen bases through 60 combined games between rookie ball (32) and Single-A (28).
Ragsdale, 22, is slashing .316/.441/.581 with 19 home runs, 51 RBI, and 31 stolen bases through 86 minor league games (60 - High-A, 26 - Double-A).