AFP"I never dreamed of being here. You just never give up. Aggie played so well, and she did an amazing job," said Williams, who was rushed to hospital last year to undergo surgery after a blood clot was found on her lungs.
Williams was a heavy favourite coming into the match and seemed set to dismantle the Polish player, who could pick up only one game in an opening set that ran for 36 minutes.
The American blew her nervous opponent off court in the first set, spraying countless winners off both flanks, but was then forced to go toe-to-toe with the Pole.
After a delay in proceedings due to rain, Williams continued to exert herself in moving 4-2 clear in the second set with a break only to appear to suffer a mental collapse as her service game and forehands seemed to desert her with Radwanska breaking back twice to force the final to a third set.
Williams lost to world number 111 Virginie Razzano in the first round of the French Open in May after being a set and 5-1 ahead in the tie-break, and it looked as if history was about to repeat itself with Radwanska, who has the consolation of being world number two after this tournament, scampering around the court with some relish.
Williams looked in trouble when she fell 2-1 behind early in the third set, but regained her composure to break for a 3-2 lead before she converted a drop shot to break for a second time to lead 5-2.
With the tension gone, she saw out the final by wining a fifth straight game. She closed out the match with a backhand winner and fell backwards onto the Centre Court turf in celebration before racing off court to embrace her family.
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