The Daily Mirror claims the England centre-back has agreed a £23million contract that runs until 2017, and headed south for a medical on Friday night.
Bolton and Chelsea decided the fee before the transfer window even opened, but it took a trip north by Blues chief executive Ron Gourlay on Thursday and seven hours of talks with the player before he accepted their salary offer.
He had wanted £100,000 a week, and at the start of the month Chelsea manager Andre Villa-Boas revealed they were a long way apart in their discussions.
But after pulling out all the stops and the intervention of Chelsea owner Roman Abramovich, the offer was raised to £80,000 a week.
Cahill was pulled out of Friday training by Bolton and has had the first part of his medical.
It will be concluded on Saturday morning, in time for him to be paraded at Chelsea's Premier League game against Sunderland at Stamford Bridge.