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In a regulatory filing, Cemig said it paid 571mn reais (US$235mn) to assume 100% of Gasmig's capital stock.
Petrobras mooted the sale in July as part of its plan to divest up to US$11bn in assets by 2018.
Gasmig holds exclusive distribution rights for piped natural gas in Brazil's Minas Gerais state.
According to Petrobras, the distributor transports 4.1Mm3/d of gas via an 850km pipeline network.
The deal is Petrobras' second major sale to Cemig in the past year.
Last October, a consortium comprising Cemig and Renova acquired Petrobras' 51% stake in hydroelectric generator Brasil PCH for US$310mn.
BNamericas will host its 11th Southern Cone Energy Summit in Lima, Peru, on November 12-13. Click here to download the agenda.