Alexander, who was also a former federal labour minister, died in Hamilton on Friday morning at the age of 90.
His body arrived at Queen’s Park on Sunday afternoon.
The public will be able to pay their respects at the lobby of the main legislative building starting on Sunday from 5 p.m. to 8 p.m., and again on Monday from 8 a.m. until 8 p.m.
A state funeral will take place in Hamilton on Friday.
Alexander is survived by his son, Keith, daughter-in-law Joyce, granddaughters, Erika and Marissa, and his second wife, Marni.
Bob Rae, the interim leader of the federal Liberals, was among the dignitaries to pay their respects to Alexander and his family at the provincial legislature on Sunday.
"Linc Alexander was a truly great Canadian and a great human being and a wonderful, wonderful friend to all of us," he said.
"And certainly to me, he was not just a friend. He was a mentor, he was an adviser, he was a tease and he was a cajoler — he always was somebody whose company I really valued and enjoyed."
Ontario NDP Leader Andrea Horwath also shared her fond memories of Alexander, recalling the time in 2004 when she went door-to-door campaigning in their home town of Hamilton and unknowingly ended up at Alexander's doorstep.
"He said, 'Well I hear you're going to win this, girl, you just keep going. You work hard and you're going to win.' It was a memory that stays with me," she recalled.
She added that Alexander would often give her words of encouragement when they crossed paths, despite their political differences.
Consumer Services Minister Margarett Best said she was still shaken after paying her last respects to Alexander, calling him a "truly great Canadian" who inspired her and other politicians of diverse backgrounds.
"I actually saw him many times in the Ontario legislature, even when he was in his wheelchair, and every time I saw him, he would hold on to my hand very, very tightly and he would always say some encouraging and some uplfiting words for me," Best said. "So it is going to be very difficult for me … to know that I will not see him in the legislature and he will not hold my hand another time, but he will still remain in my heart."
First elected in 1968
Born in Toronto in 1922 to West Indian immigrants, Alexander was a wireless operator with the Royal Canadian Air Force during the Second World War.
Alexander was first elected to the House of Commons in 1968, as the Progressive Conservative member for Hamilton West.
He served as an MP for more than a decade before leaving federal politics to become the chairman of the Ontario Workmen’s Compensation Board, which is now known as the Workplace Safety and Insurance Board.
In his later years, he served as the chancellor of the University of Guelph for five terms.
Alastair Summerlee, the president of the University of Guelph, knew Alexander for more than 20 years.
"I've described him as a man who was just larger than life," he said.
"He was a big man in height, he had enormous feet and he had an incredibly large heart and he warmed to everybody that he met."
Summerlee said that Alexander had faced many hardships in his early life, but overcame those obstacles and ultimately became a very successful and inspiring public figure.
"He began in circumstances that were definitely very impoverished, had quite a hard life as he grew up and turned that into this outstandingly successful career," said Summerlee.