The season was the first in Europe to be suspended due to the coronavirus pandemic, with the last matches played on 23 February.
Clubs will play two games a week to complete the remaining third of the season by 2 August.
The first match on 19 June is provisionally scheduled to take place behind closed doors at the Stade de Suisse in the capital Bern between title-challengers Young Boys and visitors FC Zurich.
"The ball will roll again," the SFL said in a statement, following a meeting of its 20 clubs in Bern.
The teams - 10 each in the Super League top division and the second-tier Challenge League - decided to carry on with the 2019/20 season, with 17 votes in favour.
Clubs can play warm-up matches from 6 June.