The 34-year-old, who joined Lancashire from Derbyshire two years ago, had another year to go on his contract but after talks between county officials and Cork's representatives he has signed on for a further season.
It means that Cork is set to end his career with Lancashire as they seek to make a strong impression on the County Championship first division following their promotion last season.
"We are delighted that Dominic wants to stay," said Lancashire coach Mike Watkinson. "He's one of a group of players who give us the experience that every club needs, but there is real excitement here about the potential of the younger members of the squad."
Cork could take his place amongst a youthful Lancashire side for their opening championship match of the season next week against Hampshire, last season's runners-up, at Old Trafford.
Lancashire will be without Andrew Flintoff, Sajid Mahmood and James Anderson, who are all on duty with England in India, while Australia batsman Brad Hodge will also be absent because his wife is expecting a baby.
Hodge may not be available for the start of his second season with Lancashire until early May, ruling him out of two further championship matches against Durham and Kent and the start of the one-day Cheltenham and Gloucester Trophy campaign.
Lancashire may seek to strengthen their squad, which includes 11 players under the age of 25, by signing a second overseas player and could make a further approach for all-rounder Andrew Symonds.
The Australian is believed to be interested in returning to Old Trafford following his successful season for Lancashire last season and now he has lost his place in the world champions' Test side, he could be available.