As part of the deal, 30 live matches will be shown per season, including five live Rangers fixtures from the Scottish Football League.
Coverage of the SPL begins with Celtic v Aberdeen this Saturday, with a kick-off time of 12.45pm. Rangers' first game in the Irn-Bru Third Division, away to Peterhead on August 11 at 12.45pm, will also be broadcast live.
The new deal is subject to ratification by the SPL clubs on Friday.
Barney Francis, managing director of Sky Sports said: "We've supported Scottish football since we started, over 20 years ago, and have always wanted to continue that commitment.
"Our viewers will see the SPL for five more years and our schedule includes the opening league match for Celtic.
"We will also follow Rangers as they plot their way back to Scottish football's top flight.
"Clubs now have certainty over their income and exposure across the UK and Ireland and we look forward to the new season."