The rollout widens access to a product that had been available since late June as a test to a limited group of top-tier subscribers.
X Money lets users hold deposits, send peer-to-peer payments, pay bills, transfer money by wire, and mail cheque without leaving the X app.
Deposits are held at Cross River Bank, a New Jersey-based lender that is used by several financial-technology apps, and are insured by the Federal Deposit Insurance Corporation (FDIC) up to $250,000.
Musk has said for years that he wants X to resemble China's WeChat.
WeChat, a single app for messaging, shopping and payments, is a pillar of consumer spending in China.
A post by X Money said deposits would earn an annual percentage yield of up to six percent.
This was well above the roughly four to five percent offered by the most competitive US high-yield savings accounts and far above the near-zero rates at large traditional banks.
Premium+ subscribers can earn the top rate directly, while Premium users must meet direct-deposit requirements, according to the company.
Cross River described the launch as the first government-insured banking platform in the United States built on a social network.
The launch positions X to compete with established payment apps such as PayPal's Venmo, Block's Cash App and SoFi, drawing on the app's user base of millions.
Ahead of its launch, the service drew scrutiny in Washington.
In an April 14 letter, Senator Elizabeth Warren, the top Democrat on the Senate Banking Committee, pressed Musk on how X Money would "generate revenue sufficient to pay that yield."
She also cited past FDIC enforcement actions against Cross River over lending practices.
