MoneyGram has about 350,000 outlets in nearly 200 countries. Ant Financial has more than 630 million users.
The takeover by the Chinese group will need regulatory approval from the US Committee on Foreign Investment.
The inter-agency committee reviews foreign acquisitions of domestic American assets on grounds of national security.
Eric Jing, chief executive at Ant Financial, said in a statement that the marriage of the two companies will "provide greater access, security and simplicity for people around the world to remit funds, especially in major economies such as the United States, China, India, Mexico and the Philippines".
Ant Financial has a big market share in the online payments industry in China. The acquisition could help the company extend the lead as well as expand overseas, as competition is growing in China with rival Tencent's WeChat payment system.
US-listed Moneygram's shares rose by nearly 9% on the news. The takeover has been approved by MoneyGram's board of directors.
Ant Financial's shopping spree in the US comes against a backdrop of rising tensions between China and the world's biggest economy.
Before he took office, then president-elect Donald Trump was questioning whether the US should continue its "One China" policy, sparking fury from Chinese state media. And during his presidential campaign, Mr Trump threatened to impose punitive tariffs on Chinese imports.
But Jack Ma, the founder and chairman of Alibaba, held a meeting with Mr Trump in December last year.
While President Trump has been critical of China, he said he had a "great meeting" with Mr Ma, who chose to float Alibaba on the New York Stock Exchange. The share sale in September 2014 was a record-breaker, as Alibaba raised $25bn in its initial public offering.
If the MoneyGram deal goes through, it will be Alibaba's second acquisition in the US. Last year the e-commerce giant purchased EyeVerify in a $70m deal.
EyeVerify is a start-up based in Missouri, which uses biometric authentication technology for securing user's online data and transactions.

The fire service said it had been called to more than 25 incidents following the flooding caused by heavy rain.
One woman, who lives on Carrow Road, said the water was about an inch away from her front door.
"My house is OK," she said. "I've got the towels down in preparation, but sadly the council weren't able to supply us with any sandbags."
Norfolk Fire and Rescue Service advised people not to wade into flood water, owing to the risk posed by hidden objects.
Flood water in sewers raised a drain cover near St Stephen's roundabout on the inner ring road and a car wheel jammed in the cavity.
Traffic was brought to a standstill for nearly an hour as firefighters tried to free the vehicle.
Outside the city centre, flood water made driving difficult in Sprowston and Rackheath.
People living on Hawthorne Avenue in Hellesdon grew frustrated that their road is flooded again.
One resident, Stacey Connerty, said: "Yet again it is left to local people to risk their safety to save their property and vehicles from flooding.
"This problem arises every time there is heavy rain.
"Despite repeated requests to highways and council to remedy this situation, to date nothing has been done."
There were also reports of flooding on the B1145, between Cawston and Aylsham, in Norwich Road, near to the junction with Allison Street in Marsham, at Crossdale Street in Cromer and on the A1062 at Hoveton.
Ch Insp Chris Spinks said: "Motorists should drive to the conditions and allow extra time for their journeys home.
"Standing water and heavy rainfall makes driving conditions hazardous and I would urge motorists to reduce speed, use headlights and increase the distance between you and the car in front."
Ant Financial, the digital payments arm of e-commerce giant Alibaba, is buying US-based MoneyGram for $880m (£700m).
[NEXT_CONCEPT]
Buildings and roads have been hit by flooding in Norwich.