The ceremony follows Shaukat Aziz's election on Friday in a rubber-stamp parliamentary vote boycotted by the entire opposition.
Standing alongside Musharraf at the presidential palace in Islamabad, Aziz took the oath of office in front of senior government and military officials and lawmakers.
He was due to face a vote of confidence in parliament later on Saturday, seen as a formality.
Aziz, 55, replaces caretaker Prime Minister Chaudhry Shujaat Husayn, who stepped down this week after only two months in the post.
Husayn, leader of the ruling Palkistan Muslim Leaque-Q party, was the shortest-serving prime minister in Pakistan's 57-year history.
On Friday, the lower-house vote was held up for an hour by opposition protests, after which speaker Chaudhry Amir Husayn declared "Mr Shaukat Aziz as the member who commands the majority of the house".
All the 191 ruling party members voted for Aziz - an ally of President Pervez Musharraff - while opposition members boycotted the vote following Husayn's decision to not allow their own candidate, the jailed Javed Hashmi, to attend the session.
"This is a farce, a complete farce, we don't call it election"
Hashmi is serving a 23-year jail sentence for treason after a court convicted him in April over a letter he distributed, saying it was from army officers criticising President Musharraf.
Opposition members carrying pictures of exiled former Prime Ministers Benazir Bhutto and Nawaz Sharif and wearing black arm bands, chanted slogans of "Shame, Shame," to protest against the decision.
Chanting "Restore True Democracy", members of both Islamist and secular opposition parties trooped out of the hall when Husayn announced the start of voting.
"This is a farce, a complete farce, we don't call it election," opposition MP Tehmina Daultana said.
"We are extremely upset at this undemocratic behaviour," she said as opposition MPs gathered in the lobby.