President Samia Suluhu Hassan nominated the minister to the position on Tuesday, which was announced by the parliamentary speaker Job Ndugai ahead of the approval vote.
MPs applauded as his name was mentioned.
Dr Mpango fills in the chair of vice-presidency that became vacant after President Samia became president following the death of President John Magufuli on 17 March.
Addressing parliament immediately after his name was submitted, Dr Mpango said he was surprised and that he was ready to take on the responsibility.
Philip Mpango is an economist who has held various senior positions including as a senior economists at World Bank.
Mr Mpango was among two ministers who were re-appointed by former President Magufuli as he started his second term.
Before being appointed by Mr Magufuli as a finance minister, he served as an economic adviser to former President Jakaya Kikwete.
The minister was last month seen in a viral video coughing during a press conference while paying tribute to senior government officials who had died of suspected Covid-19.