A majority decision was reached in favour of some red-ball matches, which are likely to take the form of a regionalised competition with a showpiece final at Lord's in October
The 18 counties will play red and white-ball cricket this summer following a vote on the structure of the new season on Tuesday.
Each of the clubs' chairmen were invited to pick between a mixture of first-class and limited-overs formats, and a season comprising entirely of white-ball cricket.
A majority decision was reached in favour of some red-ball matches, which are likely to take the form of a regionalised competition with a showpiece final at Lord's in late September and early October.
A version of the T20 Blast is expected to run throughout much of September, including a Finals Day at Edgbaston.
The counties' decision will now be put to the ECB board for ratification, which will come later this week.
Typically, resolutions involving the counties has required a two-thirds majority to pass, but special dispensation was given for this vote to be decided by a simple majority.
Several smaller clubs had been concerned that first-class cricket would incur additional costs in terms of accommodation, while there have been reports that some players with young or vulnerable families have been worried about the possible implications of staying away from home while Covid-19 cases continue to be regularly identified across the UK.

County cricket will return in August
Counties with larger memberships, however, had been keen to ensure that they would be able to give their members access to some first-class cricket in 2020, even if those matches are only viewable via an online stream.
Once board ratification is given, there remains a large amount of work for county administrators and the ECB organisers to get through to ensure a prompt start to the season in early August.
The ECB has been conducting full risk assessments of the county grounds over the course of recent weeks, and will continue to do so in the build-up to the new campaign.
Further question marks, relating to the local lockdown in Leicester and Welsh assembly restrictions on Glamorgan, will need to come into consideration for the schedulers - and the governing body may release the fixture list in tranches in order to allow maximum possible time for logistics to be finalised.
Many counties are hopeful they will be allowed to admit some spectators into their grounds to watch live cricket at some point in the truncated 2020 season.
As it stands, matches will have to be played behind closed doors - the ECB on Monday confirmed that the entire international programme for this summer will take place without fans in attendance - but there is genuine optimism within the game that, should the infection rate in England continue to fall, a small percentage of capacity might be permissible for the Blast in September.
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