Mr Barrett, from Styche, near Market Drayton, was involved in a collision with a Audi A3 convertible on Thursday near Nantwich.
It happened at the junction of the A51 London Road and Wybunbury Lane, near to the Boars Head at Walgherton, at about 7.50am.
Mr Barrett, who worked for global management consultancy firm ThoughtWorks, was taken to hospital in Crewe for treatment but later died.
Family and work colleagues have paid tributes to Mr Barrett, who leaves behind his wife Anne and children Charlie and Annabelle.
A statement on behalf of his wife said: "Luke, of Styche, Shropshire, was the managing director for global management consultancy firm ThoughtWorks, husband and father of two young children.
"He was tragically killed in a road traffic accident whilst cycling to work on Thursday."
A statement on behalf of ThoughtWorks said: "ThoughtWorks mourns the sudden and tragic passing of Luke Barrett. Luke was the leader of our European business, but also a friend, a colleague, a mentor and a role model to ThoughtWorkers around the world.
"Luke joined ThoughtWorks in London in 2004 as a business analyst and later served in roles as a client principal and interaction designer before stepping into the role of managing director, Europe. His contributions in spirit and in deed live on.
"We are humbled to be entrusted with the obligation to carry forth his legacy. He was an impassioned champion of ThoughtWorks' mission and will be sadly missed.
"He is survived by his wife Anne, his son Charlie, his daughter Annabelle, his parents Alison and Peter, and his sister Esther. We express our deepest condolences to his family and friends."
Cheshire Police are now appealing for anyone who saw the accident to come forward.
They can call 101 quoting incident number 117 of 26/6/14. Alternatively, information can be reported anonymously through Crimestoppers on 0800 555 111.