But the SNP said the prime minister's visit showed he was "in a panic" about rising support for Scots independence.
Mr Johnson will be in Scotland on Thursday to meet local members of the armed forces and their families.
He said troops had done "vital work" to support the NHS during the pandemic and praised Treasury job retention schemes.
Scotland's First Minister Nicola Sturgeon said she had no plans to meet Mr Johnson during his visit, but said she would continue work with his government on the "immediate priority" of tackling coronavirus.
Mr Johnson's visit comes on the one-year anniversary of him taking office as UK prime minister.
He said he had "pledged to be a prime minister for every corner of the United Kingdom", and said the response to the pandemic had shown his government's commitment to the whole of the UK.
He said: "The last six months have shown exactly why the historic and heartfelt bond that ties the four nations of our country together is so important and the sheer might of our union has been proven once again.
"In Scotland, the UK's magnificent armed forces have been on the ground doing vital work to support the NHS, from setting up and running mobile testing sites to airlifting critically ill patients to hospitals from some of Scotland's most remote communities.
"And the UK Treasury stepped in to save the jobs of a third of Scotland's entire workforce and kept the wolves at bay for tens of thousands of Scottish businesses.
"More than ever, this shows what we can achieve when we stand together, as one United Kingdom."
Although the whole of the UK entered lockdown in the same week, each constituent part has eased restrictions in a different way and at a different rate.
Phase 3 of Scotland's route map out of lockdown began last week, as pubs, restaurants, hairdressers and barbers were allowed to reopen.
Restaurants, pubs and cafes have been allowed to reopen in England since 4 July, along with holiday accommodation - including hotels, B&Bs, cottages, campsites and caravan parks.
Hairdressers have also reopened, as have libraries, community centres, bingo halls, cinemas, museums, galleries, funfairs and theme parks, children's play parks and amusement arcades.
Professional football has also resumed behind closed doors.
Mr Blackford's comments echoed a joke Ms Sturgeon had posted on Twitter, suggesting that Mr Johnson visiting Scotland would amount to a birthday present for her.
At her coronavirus briefing on Wednesday, the first minister said she had "no plans" to meet Mr Johnson on this trip, but is "always happy to meet the prime minister if he wants to do so".
She added: "We're all very focused on the immediate priority of continuing to suppress Covid and I look forward to working with the UK government on that basis.
"We have got our political disagreements, and disagreements over aspects of Scotland and the UK's future, and I'm sure we'll continue to discuss those constructively as well."
Ms Sturgeon has previously suggested that her government's response to the pandemic was helping convince Scots of the merits of independence.
In an interview with Scotland on Sunday marking her 50th birthday, she said: "As we have stopped shouting about independence, and shouting to ourselves about how we go about getting independence, and just focused on [dealing with the crisis] - it has allowed people to take a step back and say 'well actually that's the benefit of autonomous decision-making' and also 'perhaps things would be better if we had a bit more autonomous decision-making,' and to come to their own conclusions."