The firm said it plans to partner with banks and credit unions in the US to offer the "smart checking" accounts.
It said the service, to be launched via Google Pay, will allow users to add Google's analytic tools to traditional banking products.
The move follows offerings of credit cards, payment systems and loans by Facebook, Uber, Apple and Amazon.
While the products and arrangements differ, the tech giants entering the world of banking share an underlying motive: making themselves indispensable, says Gerard du Toit, a partner at the Bain & Co consulting firm.
"They're all competing for consumer attention and for their ecosystem and platform to win," he says.
Facebook has said its payment tool is a natural outgrowth of its broader aim of connecting people
Amazon's credit card and business loans are aimed at boosting its e-commerce business, while Uber Money is providing credit cards, debit accounts and money tracking tools to serve the company's taxi operations.
Facebook has said its Facebook Pay service will complement its messaging tools.
And both Google and Apple, which has teamed up with Goldman Sachs' new consumer arm, Marcus, on a credit card as part of its Apple Pay and Wallet service, want to to make iPhones and Androids essential.
Wading into financial services will also provide Google and Facebook information for their advertising business, helping to track what ads lead to purchases, Mr du Toit said.
The moves into banking are likely to add to the debates over the tech giants, which are already facing probes related to competition, data protection and privacy.
Some officials have also expressed worry about gaps in financial oversight as growing activity occurs outside of traditional banking. And in recent days, New York announced it would investigate Apple, after accusations that its credit card relied on "sexist" algorithms.
Mr du Toit said regulatory concerns represent the "fly in the soup" for tech firms.
"They will have to be very careful," he said.
In many cases, the tech firms are working with traditional banks - a sign they are aware of the potential issues, he said.
Google said its US partners, which reportedly include Citigroup, would start to offer the accounts by 2020.
"We believe our partners' regulatory and financial know-how is a great complement to our experience in building helpful tools and technology for our users," it said in a statement.