A person familiar with the negotiations told The Associated Press that a deal was in place, pending a physical. The person spoke on condition of anonymity Sunday because there was no official announcement.
Other media outlets had first reported the move, saying it was expected to be worth more than $50 million.
The Cardinals filled a need by getting a top-hitting shortstop a month after losing the World Series in six games to Boston. Pete Kozma and Daniel Descalso, while generally good fielders, are light hitters.
But this deal drew a different reaction from a couple other big leaguers.
''It pays to cheat... Thanks, owners, for encouraging PED use,'' Arizona pitcher Brad Ziegler tweeted.
''Apparently getting suspended for PED's means you get a raise. What's stopping anyone from doing it? (hashtag)weneedtomakeachange,'' free agent pitcher David Aardsma tweeted.
The 31-year-old Peralta was suspended 50 games last season as a result of Major League baseball's investigation in the Biogenesis case. He returned to the Detroit Tigers in late September and played in the postseason, both in left field and at shortstop.
Shortly before Peralta was penalized, the Tigers acquired young shortstop Jose Iglesias from Boston in a three-team trade.
Peralta hit .303 with 11 home runs and 55 RBIs in 107 games during the regular season, then batted .333 with one homer, four doubles and six RBIs in 10 playoff games.
The two-time All-Star is a career .268 hitter with 156 homers and 698 RBIs in 11 seasons with Cleveland and Detroit.
The NL champion Cardinals have been busy since the season ended. A few days ago, they sent third baseman David Freese, a hometown product and the 2011 World Series MVP, to the Los Angeles Angels for outfielder Peter Bourjos in a four-player trade.
The Cardinals cut about $45 million off last season's payroll, and wanted to plug a hole at shortstop. St. Louis lost All-Star Rafael Furcal in spring training for the whole year because of elbow surgery.
Detroit did not extend a qualifying offer to Peralta, meaning there would be no compensation draft pick involved in his move from the AL Central champions to the NL Central winners.