Former Federal Reserve Chariman Alan Greenspan told CNBC on Thursday the decadeslong bull market in bond prices is coming to an end.

"We are in a bond market bubble" that's beginning to unwind, he said on "Squawk on the Street," as new Fed Chairman Jerome Powell appeared on Capitol Hill for the second time this week. "Prices are too high" on bonds, Greenspan added. Bond prices move inversely to bond yields, which spiked higher in the new year, recently hitting four-year highs of just under 3 percent.

Greenspan is in good company in predicting a bond price bubble.

Hedge fund manager Paul Tudor Jones, in an interview with Goldman Sachs, predicted a rise in inflation and a surge in the 10-year Treasury yield. Noted bond investor Bill Gross recently said the bear market in bond prices has begun. Billionaire investor Warren Buffett told CNBC on Monday he believes long-term investors should buy stocks over bonds.

"As real long-term interest rates rise, stock prices fall," Greenspan said, but added that's probably not the cause of the recent wild market swings.

"The last few weeks are responding to the good part of the tax cut," he said, meaning that any tax-cut inspired economic growth could increase inflation, which Wall Street worries could result in the Fed raising rates more aggressively than the projected three hikes for this year to tamp down rising prices and wages.

Greenspan said he's optimistic about growth in the short term due to the new GOP tax reform law, particularly the federal corporate rate cut from 35 percent to 21 percent.

But long term, he said he's "rather dismal" due to the "gradual encroachment of entitlement spending on gross domestic savings," which is defined as GDP minus total spending.

Powell talked on Thursday about the economy and interest rates before the Senate Banking Committee. On Tuesday, before the House Financial Services Committee, he made it clear the Fed could find reason in growth or inflation to increase rates more than three times this year.

That perceived hawkish tone sent the Dow Jones industrial average about 300 points lower on Tuesday and then 380 points on Wednesday.

Just before stocks and bond prices stared tanking in the beginning of February, Greenspan said in a Bloomberg interview on Jan. 31 that he saw bubbles in both markets. "The bond market bubble will eventually be the critical issue," he said.

The stock market got off to an incredibly strong start in January after a banner 2017, but tanked in early February after a higher-than-expected wage number in January's jobs report sparked fears of inflation and interest rates rising more aggressively than projected.

Stocks on a closing basis eventually bottomed out on Feb. 8, briefly plunging into 10 percent correction territory. Since then, the Dow and have recovered about 5 percent each, based on Wednesday's close.