He declared that the country will be opened to investment and pledged to tackle entrenched corruption, in his first speech to the nation since decisively winning an election this week.
Nobel Peace Prize victor Ellen Johnson Sirleaf led the country from back-to-back civil wars but was criticized for not better tackling corruption in the diamond-rich nation.
Boakai had conceded defeat and congratulated his rival earlier in the day.
Early, President-elect Weah whose posture today appeared presidency, with is Vice President-elect Jewel Howard seated on his left hand side with glaring smiles during the conference, also used the occasion to pay tribute to those who lost their lives in the cause of the CDC, stressing, "I want us to use the occasion to call on all of us here today for a minute of silence in remembering of those Cedecians who lost their lives in the cause of our revolution".
The French presidency says in a statement that Weah accepted the invitation.
The party also congratulated the Liberian people for a peaceful and successful political transition, saying that the development was a firm and loud statement that democracy has taken firm roots not only in Liberia but also in the entire African continent.
Cold spell to stretch through New Year's
Local temperatures will remain below freezing most of the week with a blast of arctic air causing them to plummet this weekend. On Saturday there is a chance of rain and snow showers in the morning, according to the National Weather Service.
Weah, who played for a string of football clubs including AC Milan and Paris St-Germain, will be taking charge of a country experiencing serious economic problems.
According to the National Elections Commission (NEC) Weah, 51, had garnered 61% of valid votes cast from 98.1% of votes tallied.
He is set to succeed Sirleaf, Africa's first elected female president, in what will be Liberia's first democratic handover in decades.
The lawmaker representing Obokun State Constituency in the Osun State House of Assembly, Honourable Olatunbosun Oyintiloye made the submission on Friday in Osogbo, Osun State capital following the victory of the first and only African World footballer of the year, George Opong Weah in the just concluded presidential election in Liberia.
Ekweremadu urged the former World Footballer of the Year "to reciprocate the enormous goodwill and confidence reposed in him by the good people of Liberia and the worldwide community by running an all-inclusive government". She led the country from back-to-back civil wars and saw it through a deadly Ebola outbreak.