Fox wrested exclusive TV rights to major league baseball's postseason and All-Star game from 2001-2006 as part of a package worth about $2.5 billion.
The network will also retain its regular-season game of the week.
"We at major league baseball could not be happier with the result," baseball commissioner Bud Selig said. "They have been a good partner and an innovative producer of our games."
With the new Fox contract averaging about $417 million, and the remainder of ESPN's regular-season contract averaging $152 million, the two deals give baseball an average of about $570 million per season, or $19 million for each of the 30 teams.
The $570 million represents an increase of 50 percent from the $380 million baseball averaged the past five years from its contracts with ESPN and its five-year deals with Fox and NBC, which expire after the World Series.
Baseball originally hoped to capitalize on the recent trend of escalating sports rights fees by tripling its TV contracts.
NBC and ESPN, which like ABC is owned by Walt Disney Co., declined to match Fox's offer for their postseason packages by Tuesday's deadline. NBC, which will lose baseball for the second time in 12 years, broadcast the sport from 1947 through 1989, often as baseball's sole national network, then renewed the relationship in 1994.
ESPN, has broadcast baseball since 1990, began an $800 million, six-year regular season contract this season, with about $40 million attributed to this year.
Gaining the relative ratings boost from the league championship series and World Series meant more to Fox than the other broadcast networks.
Fox had the biggest prime-time ratings decline of the four major networks during the 1999-2000 season. Its average prime-time audience of 8.97 million was down 17 percent from the year before, according to Nielsen Media Research.
The last time one broadcast network owned the full baseball package was 1990-93, when CBS lost hundreds of millions of dollars in a $1.057 billion deal, partly because of a steep decline in ratings and partly because of a national recession.
Under the expiring arrangement, Fox and NBC split the league championships and alternated televising the All-Star game and World Series. Now Fox will have the TV rights to all of those events for six seasons, in addition to its regular-season rights.
The extra load of first-round playoff games could be eased by shifting some to cable channel Fox Sports Net.
In June, Fox rejected baseball's demand that the network increase its yearly payments from $120 million to $360 million, while NBC declined to up its payments from $80 million to $240 million.
Those decisions allowed baseball to try to sell its rihts on the open market. But CBS and ABC weren't interested in buying the rights at the prices baseball was offering.
The pattern of rising rights fees began in 1997 when the NBA agreed to four-year deals with NBC ($1.75 billion) and Turner Broadcasting ($890 million) for $2.64 billion more than double the league's previous deals.
In 1998, the NFL doubled its take by agreeing to contracts with CBS, Fox and Disney totaling $17.6 billion over eight years.
In November, Fox joined with NBC and TBS to win the bidding for NASCAR's TV rights. That deal is worth about $400 million a year, roughly four times what NASCAR made under its previous package.
Later that month, CBS held on to the NCAA basketball tournament by more than doubling its payments with an $11 billion, six-year contract that goes into effect in 2003.
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