Bain Capital Ventures said it led the $133 million private placement, which was the private equity firm's first purchase of cryptocurrency tokens. Other investors included Alphabet's GV venture capital arm and Andreessen Horowitz.
Formerly known as Basecoin, Basis is developing a cryptocurrency whose supply is controlled by an algorithm rather than a central bank. In contrast, bitcoin and most major cryptocurrencies have a fixed supply. Changes in demand can then send prices in wild swings.
Basis' developers say such volatility has prevented mainstream adoption of cryptocurrencies and they want to create a digital coin whose availability is tied to a measure such as the U.S. dollar or consumer price index.
"The Basis approach to creating cryptocurrency with stable value is highly differentiated," Erik Nordlander, engineering partner at GV, said in a statement. "We were drawn to invest in the Basis network because of the founding team's impressive engineering leadership and vision."
A representative for Andreessen Horowitz confirmed its investment in the private placement.
A representative for Druckenmiller declined to comment further. A spokesperson for Warsh did not immediately respond to a CNBC request for comment. Bloomberg News was first to report the investment by Warsh and Druckenmiller.
Both Druckenmiller and Warsh have criticized bitcoin for its dramatic price fluctuations.
In December, Druckenmiller told CNBC that bitcoin cannot be a medium of exchange "because you can't do transactions, particularly retail transactions, with this kind of volatility." He said he didn't own any of the cryptocurrency.
Bitcoin has lost more than half its value since December. But it remains 575 percent higher over the past 12 months, near $8,100, as of Wednesday afternoon.
The cryptocurrency's "price volatility significantly diminishes its usefulness as a reliable unit of account or an effective means of payment," Warsh, a former Federal Reserve governor, wrote in a March 7 opinion piece in The Wall Street Journal. "But a new generation of cryptocurrencies is on the horizon, some of which might possess more of the attributes of money, better satisfying bitcoin's founding purpose."
Warsh also said in the article the Fed might consider launching its own digital currency. He was one of two likely contenders to lead the central bank after Janet Yellen's term as chair ended earlier this year.