Colin Peter and his wife were walking on a beach near their resort nearly two weeks ago when he was robbed and beaten.
He died in hospital on Nov. 19.
On Sunday, police commissioner Vernon Francois said St. Lucia police have been tracking a suspect for several days.
"It essentially came to a head yesterday, when we were able to apprehend the suspect," Francois said Sunday.
"He was taken into custody and has since cooperated with law enforcement in terms of recovering some of the items belonging to the gentleman in question. I'm confident we should be able to charge him with murder."
Francois said they recovered a camera stolen during the robbery.
The suspect's name will be released when he is charged Monday or Tuesday.
Police described it as a "crime of opportunity" and said St. Lucia was a safe destination.
The 26-year-old man was arrested close to where the attack took place, police said.
Loss for community
Peter was on the island researching his family tree. He owned Montague Office Supplies in P.E.I. and had three adult children.
Merrill Scott ran a business next to Peter's for years and got to know him well.
"Colin was a very quiet, hard-working, energized person," he said Sunday. "He was just a great person to be next to."
Scott said it was a shock to hear he had been killed. He was glad there was an arrest, but said that didn't change the tragedy.
"We have lost a great businessman in the community," he said.