Close, 58, and Shaw, 54, were wed on Friday, according to the Scarborough town clerk's office.
The actress is a five-time Oscar nominee whose films include "Dangerous Liaisons," "Fatal Attraction," "The Natural" and "The Big Chill."
Close has been married twice before — to Cabot Wade from 1969-71, and to James Marlas from 1984-87. Both marriages ended in divorce.
Shaw is the founder and former head of Idexx Laboratories Inc., a publicly traded biotech company in Westbrook with more than $600 million in annual revenues.
The ceremony took place at Shaw's oceanside home on historic Prout's Neck, The Boston Globe reported.