Hancock took the oath of office in front of fellow caucus members, family, and guests in a short ceremony at Government House on Sunday evening.
"I'm honoured by the confidence my colleagues have placed in me and I'm humbled by the sense of responsibility and the opportunity to serve," Hancock said in a speech.
Minutes before Hancock took the oath, government whip George VanderBurg formally submitted Alison Redford's written resignation as premier to Alberta Chief Justice Catherine Fraser.
Fraser was substituting for Lt.-Gov. Don Ethell, who could not attend because of previously scheduled trip.
Redford was not at the ceremony, but Hancock paid tribute to her.
"She worked tirelessly to promote our province and to build its place in Canada and the world," he said.
"I want to extend my thanks, those of my colleagues and of all Albertans to Premier Redford for her service and for her sacrifice," he added, to applause.
Hancock was voted by the governing Progressive Conservative caucus to take over from Redford after she resigned Wednesday amid internal strife.
He said he understands he will only serve as premier until the party picks a permanent replacement in the coming months.
"I'm only too aware that my term as premier is finite and short," he said.
"But it's critical that we continue to build Alberta together."
Hancock, the Edmonton-Whitemud MLA, has worked for 17 years in the legislature in seven portfolios along with duties as government house leader.
He was deputy premier under Redford and later told reporters he doubts he will name another deputy premier.
"I'm not planning to make any real changes in cabinet," he said.
Hancock has already said he plans to keep his other job as advanced education minister.
PC party officials meet Monday in Red Deer to set the rules and deadlines for the leadership race.
Under party rules, the vote must be held no earlier than four months from now and no later than six.
A number of PC cabinet ministers have said they're mulling over a run for the leadership.
Hancock said he will respect the tradition that any cabinet ministers who decide to run must resign from cabinet to prevent any candidate from having an unfair advantage.
Hancock has said he won't run for the job.
He takes over a caucus that has fallen to historic lows in recent opinion polls under Redford.
The surveys suggested widespread anger and distrust with Redford over lavish spending on herself and members of her inner circle.
Her resignation came after she failed to stop growing unrest within her party and her caucus.
When she left, two caucus members had already quit, 10 more were thinking about it, and riding presidents from Edmonton and Calgary were considering a motion to ask her to resign.
Earlier Sunday, Prime Minister Stephen Harper issued a statement wishing Hancock well, saying he looked forward to working with the new premier.
Harper also thanked Redford.
"Ms. Redford was a strong steward of the Alberta economy, a strong voice in Confederation, and I commend her for her dedication and service," Harper said in the statement.
"Laureen and I wish her the very best in her future endeavours."
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