A statement released by the Prime Minister's Office Monday said the appointment was effective Aug. 31.
Brown has been a judge for 2½ years. He was appointed to the Alberta Court of Appeal and the appeal courts of the Northwest Territories and Nunavut in March 2014 after serving a year on the Court of Queen's Bench of Alberta.
According to the PMO statement, Brown's legal experience is in the areas of commercial law, medical negligence, personal injury, trusts and estates and competition law.
"Mr. Justice Brown brings to the court wide experience as a law professor and legal scholar, a barrister, and a judge at both the trial court and appellate levels. His appointment is the result of broad consultations with prominent members of the legal community and we are confident he will be a strong addition to Canada's highest court," Harper was quoted as saying in the release.
Before his appointment to the bench, Brown was associate professor and associate dean in the Faculty of Law at the University of Alberta, and served as associate counsel with the Edmonton law firm of Miller Thomson LLP. He also previously practised law in British Columbia.
Rothstein, who was appointed from Manitoba and confirmed in 2006, announced in the spring he was retiring at the end of the summer after nine years on the country's top court.
Brown's appointment would maintain the court's current regional balance, leaving it with two justices from Western Canada, including Chief Justice Beverley McLachlin, who was appointed from British Columbia.
The Supreme Court is the final court of appeal in Canada. Brown's appointment would maintain the court's full complement of nine justices, seven of whom were appointed during Harper's time in office.
Correction : This story has been updated from a previous version that incorrectly stated Justice Rothstein was appointed from Saskatchewan. In fact, he was appointed from Manitoba.(Jul 27, 2015 7:18 PM)