They had been visiting Marsili's husband and father of the girls, Gabriel Aguero, 41, who works as a chef in Qatar.
Valeria Marsili, 42, and her three daughters had their flights canceled without reimbursement on June 5 after Qatar's neighbours imposed a blockade on the Gulf state.
They had been visiting Marsili's husband and father of the girls, Gabriel Aguero, 41, who works as a chef in Qatar. They could not afford the $6,000 (5,100 euros) to buy new tickets.
After AFP reported their plight, the family received an offer of help from the son of Marcelo Simonian, a football agent representing Argentina and Paris Saint-Germain (PSG) star Javier Pastore.
The Simonians contacted the Qatari authorities and Nasser al-Khelaifi, chairman of Qatar Sports Investments, the group that owns PSG.
"My son told me what was going on, I told the story to Nasser," Marcelo Simonian told AFP by email.
"He automatically told me that he will take care of the problem and he will resolve it."
After Nasser's intervention the Qatari government "gave the new tickets for the family for free," Simonian added.
Marsili and the three girls landed back in Buenos Aires late Wednesday on a Qatar Airways flight from Doha via Sao Paulo. Aguero stayed on in the Qatari capital, where he works.
"We're tired but content," Marsili told AFP at the Ezeiza International Airport after more than 20 hours of travel.
"Fortunately this has been resolved and we're back home again."
Marsili and her daughters Bernadita and Renata -- 13 year-old twins -- and eight-year-old Emilia were welcomed at the airport by friends and relatives.
Qatar has been working to improve its image in the media after neighboring countries two months ago cut diplomatic ties with it, accusing it of links to terrorism.
Last week Qatar Sports Investments paid the record sum of 222 million euros ($260 million) to sign Brazilian striker Neymar to PSG from Barcelona.
Qatar is due to host the football World Cup in 2022 despite controversy over the selection process.