Provisional results showed the UCP had won 63 of the 87 seats in the provincial legislature.
Earlier in the month, Mr Trudeau imposed a price on carbon on four provinces without plans to tackle global warming and has made clear he would do the same for Alberta if need be.
The Alberta Party, led by former Edmonton mayor Stephen Mandel, is running a full slate of candidates.
Well-known as a pro-life and pr0-family advocate during his nearly two decades in federal politics, the Catholic Kenney has increasingly distanced himself from his those positions, and did so strongly during the election campaign.
And depending on who the victor is, Prime Minister Justin Trudeau may have to deal with another conservative premier amid a federal election year. Voters chose to back Kenney's plan to cut taxes, get tougher in the fight for pipelines and reign in government spending.
The 28-day election campaign in Canada's fourth most populous province centred around its uneasy economic future.
"A Kenney-Trudeau showdown over energy and climate policy raises a number of significant risks for investors, as further delays, lawsuits and federal-provincial negotiations will make final resolution of key policy issues and project approvals harder to achieve", the Eurasia report said. He has also threatened to hold a referendum in 2021 to remove equalization, a program that forces "have" provinces to give money to Ottawa to distribute to "have not" provinces.
"It ended a 44-year dynastic political climate that you have in Alberta", said Sally Hausser.
Trudeau was asked in Kitchener, Ont., earlier Tuesday whether he was concerned about his climate plan should Kenney win.
Throughout his campaign, Kenney said his first order of business would be to introduce the Carbon Tax Repeal Act.
Her government brought in a carbon tax created to help cut emissions of greenhouse gases.
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The UCP won a majority government after one of the most divisive campaigns the province has ever seen.
"We have in Ottawa a federal government that has made a bad situation much worse".
Mr Kenney, a 50-year-old former federal cabinet minister, vowed to take more decisive action on jobs and the economy.
The Alberta premier-designate's stance on the carbon tax means the four premiers now against the program will have another ally in their fight against Ottawa.
Currently, Saskatchewan is the only other province with a two-party system.
Moe echoed that sentiment with his own congratulatory tweet to Kenney on Tuesday. He has said he will proclaim a law passed by Notley's government but never proclaimed.
Outgoing premier Rachel Notley said she would stay on as NDP leader.
Kenney supports new oil pipelines, including the Trans Mountain expansion that will connect the Alberta oil sands to the Pacific coast, and triple the amount of crude reaching the Pacific Coast.
In response to those delays, Kenney has vowed to "turn off the taps" or cut off oil and gas shipments to B.C. if they obstruct pipeline construction.
"Under the Notley regime, parental rights, religious freedom and free speech were gravely curtailed", said Campaign Life Coalition national president Jeff Gunnarson.