They were elected at the three-day CPI State Executive and Council meeting, which concluded here last night.
Also, former MLA M Arumugham was elected treasurer.
CPI national secretaries D Raja and Dr Narayana were present.
R Mutharasan had already been elected the party's Tamil Nadu unit secretary during its state conference held at Mannargudi in March last.
Mutharasan, Subbarayan and Veerapandian were among those elected to the State Council, party sources said.
A 31-member State Executive Committee, which will have three-year tenure, was also formed, they added.
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