Police had been treating the death as a homicide since June.
Beckett has an ex-wife, Wendy Sail, and four children aged between 17 and 5 in New Zealand.
A family member declined to comment on the charges.
Napier mayor Barbara Arnott said: "I'm aware that his wife and children are here and I think that it's pretty traumatic for them.
"I don't think he made a contribution to the council or this city," she said of the one-term councillor who served from 1998 to 2001.
When elected to council, Beckett claimed he would be a "bit of a stirrer".
His parents died by the time he reached his early 20s and he inherited a home in Waipatu, Hawke's Bay.
Beckett also ran a tourism business taking tours to Cape Kidnappers.
After moving to Canada, Beckett drove a school bus for Pembina Hills Regional School Division, while Letts Beckett was a teacher at Dapp Elementary School near Edmonton, Alberta.
Friends from the small town of Westlock, Edmonton, where the couple lived, were shocked when they heard of the arrest.
Dapp Elementary School principal Wendy Sinski, who worked with Letts Beckett for 10 years, described her as a "dear friend".
"She was an incredible and wonderful lady."
She said there was no suspicion at the time of Letts Beckett's death.
"It just seemed like a lot of unfortunate circumstances that led to that.
"Nothing was said at the time."
She was an "excellent" teacher, said Sinski.
She visited Beckett soon after his wife's death and said he was shaken - and that there was nothing to suggest that he may have killed her.
Letts Beckett's family released a statement saying they were relieved the investigation was over.
"We are relieved that the investigation is over, as a family we are waiting for the justice system to take its course. Please respect our family's privacy as we remember the anniversary of Laura's death."
The Ministry of Foreign Affairs and Trade said it was not aware of the arrest of a New Zealander in Canada.
