Mr Weah got 78% of the vote for the Montserrado county seat, which includes the capital Monrovia.
He beat Robert Sirleaf, the son of President Ellen Johnson Sirleaf, who took nearly 11%.
Low turnout in the poll, which was first planned for October, was blamed on concerns about Ebola.
Strict health controls were in place to try to prevent the spread of the disease.
Those who came to polling stations had their temperature taken, were told to stand a metre (3ft) apart and wash their hands before and after voting.
Liberia has been one of the countries worst affected by Ebola, with almost 3,400 deaths, the UN says.
Other winners in the senate elections include Jewel Howard-Taylor, the ex-wife of the jailed former president Charles Taylor, and the former rebel leader Prince Johnson. Both retained their seats.
The National Elections Commission chairman, Jerome Korkoya, called the conclusion of the vote "the end of a crucial journey".
Mr Weah won the first round of the 2005 presidential election, losing the runoff to Ms Johnson-Sirleaf.
He is the only African to be named Fifa's world player of the year, winning in 1995.

The Shrimps lost their opening game of the season at newly-promoted Grimsby but then knocked Championship side Rotherham out of the EFL Cup 5-4 and have won three straight league games.
"It's nice but it is early days," 40-year-old Bentley told BBC Radio Lancashire.
"You're never too high and never too low and I keep saying that."
He added: "It's important everyone keeps their feet on the ground - likewise when you have a sticky spell that everyone keeps check and sticks together."
Kevin Ellison, 37, got the only goal of the game as Morecambe's 1-0 win at Yeovil on Saturday moved them to the top of the league.
"People say about his age and this and that but if you work with him day in, day out you see how he rubs off on other people," added Bentley on Ellison. "His desire, his attitude towards training and his own recovery and own professionalism, he's a credit to himself and his family.
"A lot of young people should look at him up and down the country because he is that good at what he does."

Residents awoke from a night of colourful fireworks to find the city covered in a thick grey blanket of smog and authorities warned that pollution levels were critically high.

David Sole, 33, of no fixed address, had denied murdering Jonathan Ellison but was found guilty at Lewes Crown Court of beating him to death.
Denise Antonia, 33, of Appledore Road, Brighton, was cleared of murder but found guilty of assisting an offender. She was jailed for five years.
Mr Ellison was found dead in his flat in Gloucester Street on 8 April 2011.
Sole and Antonia were arrested in Winchester, Hampshire, on 16 April following an investigation by Sussex Police's major crime branch.
Following the two-week trial, Sole was told he would serve a minimum term of 18 years.
Det Ch Insp Trevor Bowles said: "Jon Ellison was killed by a man who had befriended him and who he trusted.
"His trust led to his death, as the result of a motiveless but brutal drug and drink-fuelled assault, which caused some of the worst injuries any of us have ever seen."
Mr Bowles said Mr Ellison was a "vulnerable man with many health and personal problems" but he was regarded as "a kind and trusted person".
In a statement issued through Sussex Police, Mr Ellison's brothers said: "He did not deserve to be taken in such a brutal way.
"It was completely at odds with his kind and gentle spirit."

Imani Wiltshire was discovered on the lower deck of the bus in Stratford, east London, on 28 September.
She was taken to hospital where she was pronounced dead. A post-mortem examination found she died from head injuries.
Rosalin Baker, 25, and Jeffrey Wiltshire, 52, of Manor Park, pleaded not guilty to murder at the Old Bailey.
They also denied charges of causing or allowing the death of their child.
A trial date has been set for 13 March at the same court.
The former football star George Weah has won a landslide victory in Liberia's senate elections, in polls disrupted by the Ebola outbreak.
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