The Sun says the staggering one-year extension makes England star Cole the world's highest-paid left-back.
A Chelsea insider said: "Ash is getting around £200,000 a week but he is worth every penny. Everyone is pleased it has been sorted at last."
But 32-year-old Cole's bid to bag a longer deal beyond 2014 has ended in failure.
Blues owner Roman Abramovich is adamant all players over 30 will be offered only one-year extensions.
"We keep a world-class player and he gets a good pay rise that keeps him up with the game's top earners."