The ballot was mailed out this week to more than 500 voting members of the Baseball Writers Association of America. The results were announced Saturday.
Eckersley had a dual career as a starter and reliever and finished with 197 wins and 390 saves.
Two other former MVPs, Kevin Mitchell and Terry Pendleton, also are among the first-year candidates eligible in 2004, as are Paul Molitor, Cecil Fielder, Dennis Martinez, Doug Drabek, and 1993 World Series hero Joe Carter.
The other first-time candidates are Juan Samuel, Jim Eisenreich, Danny Darwin, Jimmy Key, Randy Myers, Dave Stieb, and Bob Tewksbury. Eight other former MVP winners, Andre Dawson, Steve Garvey, Keith Hernandez, Don Mattingly, Dave Parker, Jim Rice, Ryne Sandberg, and Dale Murphy, are holdovers.
Election results will be announced Jan. 6.