Some shoppers queued from as early as 03:30 to be first in line for the opening of the sales.
Silverburn in Glasgow said it was expecting about 60,000 shoppers on Saturday - up about 10% on last year.
General manager David Pierotti said: "Boxing Day is always one of our busiest days of the year."
He said: "We were delighted to welcome shoppers on the official start of the post-Christmas sales, with queues from 04:30."
Glasgow Fort said people started queuing outside the centre's Next store from 03:30, with about 300 waiting when the doors opened at 06:00.
Crowds also formed outside Marks and Spencer ahead of its 08:00 opening.
In Edinburgh, shoppers traditionally flock to luxury department store Harvey Nichols for cut-price designer goods.
About 100 people queued outside the St Andrew Square shop ahead of its 10am opening, with handbags among the most sought-after purchases.
Around 57,000 shoppers were expected at Aberdeen's Union Square.
At intu Braehead, outside Glasgow, manager Gary Turnbull said it was the busiest start to the Boxing Day sales the centre had seen "for years".
Ian McLelland, director at the EK centre in East Kilbride, said: "The centre has been packed all day. Despite many retailers starting their sales pre-Christmas, shoppers are well aware that there are still plenty of deals to be found across fashion, toys, games, jewellery and electronics."
Shopping centres across Scotland have reported their busiest Boxing Day in years as bargain hunters took advantage of post-Christmas discounts.