ScotRail will be running more than 90% of its normal services from Monday.
The operator says all routes will have normal early morning, late night, and peak services, and 100% of normal capacity will be provided during peak times.
But many seats will need to remain empty to maintain physical distancing.
It comes ahead of the expected reopening of schools from August 11, which could see an increase in the number of passengers.
Earlier this week the operator announced that physical distancing on its services would reduce from 2m to 1m.
David Simpson, ScotRail operations director, said: "Thanks to the hard work of staff across Scotland’s railway, we’ll operate as close to a normal timetable as possible from Monday.
"Like businesses across the world, we continue to face challenges caused by coronavirus, but we will have every available train in service from 3 August.
"We do need everybody to continue taking personal responsibility for their travel choices, because physical distancing can’t be guaranteed. Customers who do travel with ScotRail should follow our five rules for safer travel, including the wearing of a face covering on trains and at stations."