Thomson has cited "family reasons" for his decision that shocked the Seasiders Committee at a meeting earlier this week.
A stunned chairman, Tam McCreadie told the Carrick Gazette on Tuesday afternoon: "We were all quite shocked at the news.
"Billy has done a terrific job since he arrived and we would like to thank him for that."
Thomson arrived at Hamilton Park in 2006 from Ardeer Rovers when the club were struggling in the Super League First Division.
Although he wasn't able to save the club from the drop, he built his own side which won a quick promotion from the Ayrshire District League.
It is understood that his assistant, Brian McCluckie, has been offered the manager's role and an answer was expected last night (Wednesday).
The Gazette also believes that Ernie Dawe would be offered a role as Brian's assistant - should the former Kilwinning Rangers man take on the role.
The club is looking to secure Thomson's replacement as quickly as possible and avoid any uncertainty over the current playing squad's future.