Maryam Nawaz thanked the people of Pakistan and said, "Inshallah, her father wouldn't disappoint the people".
"The wise youth chose to side with PMLN who delivered and will deliver InshaAllah ! Well done! Let's together build a Roshan Pakistan !" Maryam tweeted on a microblogging website.
Taking a swipe at Pakistan Tehreek-e-Insaf, which had vocally criticised Sharif during the campaign, Maryam said, "Dear PTI friends ... Politics of abuse, foul-language and allegations didn't work... Try something else next time. For now let's build Pak!"
Sharif, 63, served as premier during 1990-1993 and 1997-1999 but was ousted from office before he could complete his term - once on corruption charges and later because of a military coup led by Pervez Musharraf.
After being deposed in 1999, he was jailed and sent into exile to Saudi Arabia.
He returned to Pakistan shortly before the 2008 polls and rebuilt his party, which has also returned to power in Punjab, the country's most populous and politically crucial province as it has more than half of the seats in the lower house of parliament.