The new three-year deal, which runs from 2016 to 2018, will see the pan-European broadcaster replace Sport TV as Formula One's Portuguese broadcast partner.
The agreement covers all races, qualifying and practice sessions, with Eurosport set to have access to multiple live feeds including coverage from on-car cameras and helicopter footage.
"F1 is one of the biggest sporting brands and the biggest event in the motorsport calendar," said Eurosport chief executive Peter Hutton.
"Securing these exclusive rights in Portugal further demonstrates our strategy to acquire key properties on a local as well as a pan-regional level, along with our commitment to put the greatest events, and capture the best sporting moments, on Eurosport. This is already proving successful and we are seeing double digit audience growth across Europe."
The acquisition of Formula One further bolsters Eurosport’s motorsport offering, which also includes the MotoGP, Le Mans 24 Hours, the FIA WTCC, the World Superbike Championships and the FIA 'Formula E Championship.
Next year’s Formula One calendar has a provisional line-up of 21 races, with the season starting in Australia in April and culminating in Abu Dhabi in late November.