First Minister Nicola Sturgeon announced the plan to offer lateral flow tests earlier this week, after the Scottish Government faced calls to match a similar policy announced in England at the weekend.
But while the English scheme will begin on Friday, the measure will not come into force in Scotland until the end of April, in line with the easing of lockdown restrictions.
England is set to see an earlier easing, with non-essential shops and outdoor hospitality allowed to open from Monday.
The tests, which offer quick results but are known to be less reliable than the alternative PCR tests, will be available free to all over-18s without symptoms.
Asked if Scotland would begin the testing on the same day as England, Professor Leitch said he “does not anticipate it being as quick as that”.
“What we anticipate is this being is part of the future openings,” he said.
"So this will coincide with, for instance, moving to the levels, and allowing people to do more stuff - this will be an added layer of protection on top of that going out more and being able to see your family more.”
Prof Leitch said he would like to see as many people as possible take the tests regularly.
“We've been pleased with how it's gone in schools with teachers, and senior pupils, and we're anticipating that getting even better when they go back. S1 to S6 will be offered it from the 12th, some of them, and the 19th for others,” he said.
He added: “It's not magic, it's not a single solution, but it just adds a layer of protection for you as you go out and about, whether it’s your journalistic business, your call centre business, or even going to the garden for a barbecue to see your family.
“It would just allow you to be a bit more sure that you don't have the virus.”