MEXICO CITY, April 27 (Reuters) - Former government minister Luis Tellez was named as president of Mexico's stock exchange on Monday, the bourse said.

Tellez, who ran a Mexican conglomerate and worked in private equity in between government posts, resigned as communications and transport minister in March after a radio show aired a compromising phone recording of the minister.

Tellez was recorded saying he knew about a huge corruption scandal under former President Carlos Salinas de Gotari in the 1990s when he was a junior minister in that government.

Tellez, who did not deny the conversation, will take up his new post on May 5, taking over from Guillermo Prieto who has held the presidency since 2001.

Mexico's stock exchange (BOLSAA.MX: Quote, Profile, Research), known as the Bolsa Mexicana de Valores or BMV, went public last year and is the second largest Latin American market after Brazil.

Despite its initial public offering, the exchange has not expanded as fast as other regional bourses like Brazil and Chile as a culture of keeping businesses within families has held back its growth, experts say.