Rajapakse's decision to make Pillayan the chief minister could cause a split in the ruling party coalition which won the polls with its Muslim leaders saying they would operate as independent members in new provincial council.
Both Pillayan, who heads the TMVP, a grouping of Tamil Tiger defectors, and Muslim leader M.L.A.M Hizbullah had staked a claim for the chief minister's post.
The poll, the first for the eastern provincial council, was won by the governing United People's Freedom Alliance party (UPFA) and its allies.
The government wrested control of the eastern region in a military campaign last year that ousted the Tigers with the help of defectors including Pillayan.
Opposition parties have vowed to challenge the poll result, alleging vote rigging and intimidation by the government and Pillay