Weah won 61.5 percent of the votes in December's election run-off, beating outgoing vice president Joseph Boakai who garnered 38.5 percent of the ballot.
Voter turnout was 55.8 percent, or just over 1.2 million people, according to the election commission.
The former world footballer of the year succeeded Ellen Johnson Sirleaf, Africa's first elected female president.
Weah entered politics after retiring from football in 2002 and run for the presidency in 2005 losing to Sirleaf.
The last peaceful transfer of power between two democratically elected presidents took place in Liberia in 1944, when president Edwin Barclay was replaced by William Tubman.
The swearing-in ceremony at a stadium near the Liberian capital, Monrovia was attended by more than a dozen African and foreign dignitaries, including heads of state from Ghana, Nigeria, South Africa, Mali, Ivory Coast and Guinea.
Many Liberians regard the 51-year-old as a hero for his incredible rags-to-riches tale. He was born in a slum in Monrovia, but found fame in international football.
Weah has promised to eradicate corruption in the country of four million people and bolster the weak economy.
Monrovia is highly dependent on exports of iron ore and rubber, which have recently plunged in prices. The country is also trying to overcome the effects of the Ebola outbreak, which left more than 4,000 people dead.
Liberia is one of the poorest countries in the world with 80 percent of the population living on less than $1.25 a day.