The Bushes, who lived in Texas and Maine, both died in 2018.
Republican Sen. Susan Collins of Maine said the coin will pay tribute to the Bush legacy of "courage, duty, honor, and compassion" and serve as a reminder of their contributions to the country.
Sponsors include Collins and Republican Sens. Ted Cruz and John Cornyn of Texas, Rob Portman of Ohio and independent Sen. Angus King of Maine.
The Presidential $1 Coin Act requires the U.S. Treasury to issue new $1 coins in honor of the nation's deceased former presidents and directs the treasury to issue pure-gold bullion coins depicting first spouses.