The St. Louis Cardinals have signed John Tudor, the top left-handed pitcher in the major leagues last year, to a three-year contract, the National League club announced yesterday. The contract reportedly is worth more than $3 million.

Tudor, 32, has been working out with the club since Saturday, when pitchers and catchers reported for spring training at the Cardinals' Busch Complex in St. Petersburg, Fla. A Cardinals spokesman said terms of the contract would not be disclosed.

Tudor, acquired by St. Louis before the 1985 season, won 21 games to help the Cardinals win the National League pennant. He also won two World Series games but was the losing pitcher in the seventh game against the Kansas City Royals. During the regular season, he had a league-leading 10 shutouts, one short of Sandy Koufax's major league record.

He finished second to Dwight Gooden in the voting for the National League's Cy Young Award . . .

Dave Winfield and Rickey Henderson, two-thirds of the New York Yankees' starting outfield, were missing as the American League club held its first full workout of the spring in Fort Lauderdale, Fla.

The Yankees said that Henderson was having root canal work done on his teeth in Oakland and was expected to arrive Saturday. Winfield's lawyer, Jeffrey Klein, called the team later in the day and said Winfield has been involved in public service matters involving the Winfield Foundation and will be at Friday's workout. . . .

Carlton Fisk has gone from behind the plate to left field as the Chicago White Sox opened spring training for the full squad in Sarasota, Fla.

"Lack of involvement will be the biggest change," said Fisk, a 16-year veteran who was on 10 American League all-star teams as a catcher and is third on the all-time home run list for catchers with 257.

White Sox management believes Fisk, 38, who hit 37 homers last season and drove in 107 runs, will add two to three more years to his career by playing left.