The GOP tax overhaul means a $4,000-a-year pay raise for the average family starting in about 2021, a top economic advisor to President Donald Trump told CNBC on Monday.

Kevin Hassett, chairman of the Council of Economic Advisers, had projected the $4,000-a-year benefit last October. The tax overhaul was signed into law in late December.

"Now we've passed the bill, and now we're expecting in over three to five years, we'll see the $4,000," Hassett told "Squawk Box" on Monday.

"It's $4,000 that will be reached in total once the economy reaches [a] steady state, and once you get it, it stays in your pay," DJ Nordquist, the council's chief of staff, told CNBC after the interview.

Hassett also said Monday he and President Donald Trump were surprised at the speed of the announcements by U.S. companies about employees bonuses and wage increases.

By contrast, Democratic former Treasury Secretary Larry Summers and other big names have suggested the employee bonuses are simply a "gimmick," and the tax cuts are not reflective of long-term hopes for prosperity.

Summers has also called the Trump administration's prediction of $4,000 wage increases as "an absurdity," arguing that "record highs" in corporate profits show that companies don't need an incentive to increase wages.

Summers ran Treasury during Bill Clinton's presidency and was director of the National Economic Council under former President Barack Obama.

But Hassett, a former economist at the American Enterprise Institute and ex-senior economist at the Federal Reserve, sees some of the extra profits appearing in workers' paychecks by next January.

"Historically, if you look what happens when after-tax cash flow happens, ... then we see about a third of that going to workers," Hassett said. "It'll be interesting to come back at the end of the year, watch the wage increases that we've seen, watch the profit increases that we've seen after tax and compare the two."

Before his appointment, Hassett had also been a consultant to the Treasury Department and an advisor on presidential campaigns, including Republican Mitt Romney's unsuccessful run in 2012.