Moynihan cited consumer spending figures from the millions of households using his lender's credit and debit cards: While transactions collapsed by about 30% in April, it was down by only 5% to 10% in May.
"You're starting to see the economy come out of the hole," Moynihan told CNBC's "Squawk Box" co-host Becky Quick. "You're seeing us come out of the depths of where we were in April, and that's good news."
Despite a record surge in unemployment during the pandemic, Bank of America customers have been helped by the government's stimulus checks and enhanced unemployment benefits, which supported the spending rebound, Moynihan said. Stocks have climbed this week on optimism about the reopening of the economy, and on Wednesday the S&P 500 closed above its 200-day moving average for the first time since early March.
"The real difference is the amount of stimulus that has gone into the economy," Moynihan said.
Balances of checking accounts below $5,000 had 30% to 40% more money in them compared with 12 weeks ago, he said.
Now, as states have begun to reopen, businesses like dentists' offices are taking in customers and "that's good news, that will bring back parts of the economy," he said.