The rights enable BSkyB to offer full delayed coverage or extended highlights of all Barclays Premiership matches not broadcast live.
The three-year deal will kick-off with the 2007/08 season and run up to and including the 2009/10 season.
Sky won the rights in a joint bid with BT worth an estimated £84.3m.
BT will use the on-demand games for BT Vision, its new broadband TV channel it intends to launch later this year.
Both BT and Sky will put the games avaiable for viewing after 10pm on each match day.
Dan Marks, CEO of BT Vision, said: "This is a landmark moment for sports viewing in the UK as BT Vision customers will have great control, convenience and choice over the games they want to watch without the need for an upfront subscription."
Vic Wakeling, managing director of Sky Sports, said: “These near-live rights, added to the live matches, give Sky Sports unrivalled Premiership coverage.
“We can now promise Football First until the end of the decade and new ways of watching games, on demand, through broadband.
“Our recent live deal brings more live Premiership matches to Sky Sports with the best games and biggest head-to-heads.”
Earlier this month, the FA Premier League awarded Sky four packages of live rights, each of 23 matches, for seasons 2007/08 to 2009/10. All 92 matches each season will be shown live on Sky Sports.
The remaining two packages went to Irish channel Setanta.
