The 21-year-old was detained while trying to cross into the United States at a border crossing in Lyndon, in the northwestern US state of Washington, Edmonton police superintendent Bob Hassel said.
"We're grateful to the border officials at Lynden, Washington, for their excellent work in arresting a man we believe was armed and extremely dangerous," Hassel said.
The 21-year-old, who was driving a blue pickup truck at the time of the arrest, faces three counts of first degree murder and one count of attempted murder.
Baumgartner and the victims all worked for G4S, a security company that was replenishing funds at an ATM inside the HUB Mall, a shopping center and student residence on the university campus.
Earlier on Saturday, Baumgartner's mother had pleaded with him to surrender.
In a letter made public by police, Baumgartner's mother apologized for an argument the two had and begged him to "do the right thing."
"You're not alone Trav. Please." Sandy Baumgartner wrote, promising to support him no matter what. "I love you and I want to help you. Call police now and end this peacefully."