The move beyond Level 0 means no venues will legally be required to shut, allowing nightclubs to reopen for the first time since March 2020.
The Scottish Licensed Trade Association (SLTA) said the end of the one-metre distancing rule would also allow many smaller venues to reopen.
Colin Wilkinson, SLTA managing director, said: "This is the best news the licensed hospitality industry has had for over a year - it's the news we've been waiting for and I'm sure there will be a few champagne corks popping to celebrate, at long last, a return to near normal trading.
"We are particularly relieved that physical distancing restrictions can be dropped as the one-metre rule made trading very difficult for some premises, particularly smaller ones - premises can now get back to operating at maximum capacity.
"However, while we understand why the Scottish Government wants to keep some mitigation measures in place, including the mandatory wearing of face coverings in some public spaces and a need for hospitality and indoor venues to continue to collect customers' contact details, we hope that this is a short-term requirement."
The Scottish Beer and Pub Association also welcomed the announcement, but noted around 285 pubs north of the border are estimated to have closed for good since the start of the pandemic.
The association's chief executive Emma McClarkin said: "This is the confirmation that so many in our sector have been desperate to hear.
"It is fantastic news for our pubs, which have suffered more than most sectors over the last 15 months.
"Over 200 Scottish pubs will now be able to reopen their doors for the first time from next Monday."
Leon Thompson, of UK Hospitality, said: "Some of our businesses can, at long last, reopen their doors and welcome back customers.
"Many more can begin to look at increasing capacity with the end of physical distancing.
"However, it is not clear yet how the mandatory wearing of face coverings might continue to impact on venues where customers are likely to be standing, including in pubs and nightclubs.
"Businesses need more detail, along with a complete set of guidance from the Scottish Government - and they need it quickly."