Cain and Bumgarner are signed long-term, while Lincecum received a $35 million, two-year deal last month.
Hudson spent his first six major league seasons with the A's, who selected him in the sixth round of the 1997 amateur draft out of Auburn.
Oakland traded Hudson to the Braves in December 2004 and he pitched nine seasons in Atlanta. The three-time All-Star earned NL Comeback Player of the Year honors in 2010 after he returned from elbow ligament replacement surgery to go 17-9 with a 2.83 ERA. He had back surgery for a herniated disk in November 2011.
The Giants had been eager to find an experienced starter to fill in the rotation. Zito just finished a $126 million, seven-year contract and had his $18 million option declined for 2014. Vogelsong's $6.5 million option for 2014 was declined by the club.
Hudson is 205-111 in a 15-year career and was coming off a $36 million, four-year contract.