Variety reported that Netflix won a "three-way bidding war that had recently narrowed from the six major studios to Netflix, Amazon and Disney".
Netflix boss Ted Sarandos said he was "thrilled to welcome" the "master storytellers".
Benioff and Weiss added how "grateful" they were to HBO, the US network that broadcast Game of Thrones.
HBO is also going to broadcast the forthcoming Game of Thrones prequel, which will be shown in 2020 at the earliest.
"We've had a beautiful run with HBO for more than a decade and we're grateful to everyone there for always making us feel at home," Benioff and Weiss added.
They explained they had found common ground with Netflix executives, including Sarandos, after talking to them in recent months.
"We remember the same shots from the same 80s movies; we love the same books; we're excited about the same storytelling possibilities," they said. "Netflix has built something astounding and unprecedented, and we're honoured they invited us to join them."
Variety said no financial amount was mentioned for the development deal. But it added that similar deals between Netflix and figures including Grey's Anatomy creator Shonda Rhimes were "said to have been worth nine figures".
Boost for Netflix
In July, Netflix revealed it had attracted fewer paid subscribers than expected in the previous three months, blaming price rises.
Shares in the company sank 10% after it added 2.7 million new customers worldwide in the April-June period, well below expectations.
Benioff and Weiss have had huge success with Game of Thrones, earning 47 Emmy awards and 160 nominations for the show, which is based on the books by George RR Martin.
The fantasy drama - which is up for a further 32 Emmys next month - ran for eight seasons, ending earlier this year. The final season got mixed reviews, however, with some fans disappointed with how the show ended.