Byrne founded the construction group in 1969 with his brother Johnny and was chief executive of the business.
Byrne Bros (Formwork) grew rapidly to become one of the best known names in the concrete frame sector.
Tony Dowle, group managing director, said: “All the members of staff send their deepest heartfelt condolences to every one of the Byrne family at this most difficult time.
“Patsy was an immense character who touched the hearts and minds of everyone he came into contact with.
“He built the Byrne Group of companies into one of the most robust and respected businesses in its specialist fields in UK construction. He will be very sadly missed.
“Continuity measures have been put in place to ensure the continued and successful operation of the Byrne Group businesses.
“The Directors will be contacting our clients personally in the near future.”
Byrne was also a prominent figure in the racing world and his sudden death over the weekend has prompted a flood of tributes.
Champion jockey Tony McCoy tweeted: “Sad news about Patsy Byrne, a great man and friend.
“Big loss to the racing and greyhound world, thoughts with his wife Bridget and family.”