He said: “If we’re brutally honest, you haven’t had the Scottish Labour Party you deserve.
“With rising injustice, inequality and division, I’m sorry we haven’t been good enough. I will work day and night to change that, so we can build the country we all need.”
Sarwar said his election, as the first person from an ethnic minority to lead a UK party, was a testament to Scotland.
“That doesn’t say something about me,” he added. “That says something great about Scotland and its people. But the fight for equality is far from over.
“I’ll work with all our diverse communities in Scotland to rebuild the country we love.”