The council near Liverpool said it is the first local authority in the country to mandate mental health checks before awarding work.
Councillors decided on the new policy after meeting up with with ex-Everton and England international footballer Trevor Steven.
Steven is a Mental Health Ambassador for software provider Causeway Technologies who are campaigning on the issue.
Council Leader, Cllr Mike Wharton said: “The suicide rates of young men working in construction are shockingly high and it’s time to do more.
“Asking contractors to consider the mental wellbeing of their staff, and making this a prerequisite of being awarded contracts, will help make inroads into the challenge of reducing the numbers of suicides and people experiencing mental health issues at work. We are the first council in the country to take this approach and I hope many more will follow.”
One contractor said: “Getting people to chat about their mental health is obviously a good thing but this is going way beyond that with a council leader imposing new tender conditions on contractors.
“As a responsible employer we can encourage people to talk about their issues but a lot of the narrative seems to be that somehow construction is responsible for these high suicide rates when surely there are a lot of other factors at play rather than someone’s occupation.
“This smacks of more unnecessary box ticking and PR by a council rather than something which will have a lasting effect on the people who most need help.”