The deal was approved by Major League Baseball and the teams' medical staffs.
Rolen, a seven-time Gold Glove winner, had a disagreement with St. Louis Manager Tony La Russa. He waived his no-trade clause and the Cardinals explored trading Rolen during the Winter Meetings in December, to no avail.
Rolen, the 1997 rookie of the year, is a career .283 hitter with 261 home runs and 1,012 RBI in 1,505 games between Philadelphia and St. Louis.
Glaus has 277 homers with 778 RBI and a .254 average in 10 seasons with the Angels, Diamondbacks and Blue Jays.
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