By James Ramage and Chiara Albanese 

A rally in the dollar is picking up steam, as signs of accelerating U.S. growth bolster investor expectations that the Federal Reserve in the coming year will raise interest rates for the first time since the financial crisis.

The dollar ascended to a new eight-month high against the euro on Thursday, continuing a rally that has driven it up 4.3% against the common currency since early May.

But more telling, investors and analysts said, was the dollar's performance relative to other currencies, where it has been dormant or in decline in recent months. The dollar rose against the Japanese yen by the most in four months on Wednesday after an initial reading on second-quarter U.S. growth was stronger than expected. The data also drove the dollar to a one-month high against the British pound.

This broad-based rise in the dollar is vindication for investors whose bullish bets were derailed earlier in the year by softness in the U.S. economy and doubts about the trajectory of the Fed's monetary policy.

A slight change in the way the Fed addressed inflation in its statement following its policy-setting meeting this week gave some investors even more reason to be optimistic about the dollar. The Fed said inflation has "moved somewhat closer" to the central bank's longer-term target. Previously, the Fed said inflation had "been running below" target.

For many investors, that change cemented the belief that the Fed was moving toward its first rate increase since 2006, in contrast to other major central banks in regions still struggling to shore up growth. Rising rates tend to lure investors to a currency because they boost returns on some assets denominated in that currency.

"We may be at the start of the shift," said Eric Stein, co-head of the global income team at Eaton Vance Management, which oversees $12.8 billion in assets and is betting on the dollar's rise. "The theme of diverging developed-market central banks hasn't played out so far in 2014. It is now playing out in currency-market price action."

Many market strategists and investors expect the Fed to raise rates in the middle of next year. The likelihood of a rate increase at the Fed's June 2015 meeting was 57% on Thursday, based on trading of Fed-funds futures.

At its meeting, the Fed again cut back its bond-purchase program by $10 billion, to $25 billion a month, as expected.

In late New York trading on Thursday, one euro bought $1.3390. That is the highest level for the dollar since Nov. 8, 2013. One dollar bought 102.80 yen, mostly unchanged from Wednesday, when the dollar closed at its highest level against the Japanese currency since April 7. The greenback rose 0.2% against the pound, which late Thursday bought $1.6880, the highest since June 12.

Any sharp slowdown in the U.S. economy would likely prompt the Fed to delay an interest-rate increase or resume easing, investors say. Jobs growth remains key and a string of disappointing monthly reports on U.S. nonfarm payrolls could derail the dollar's rally, they add. The report on hiring in July is due Friday, with economists, on average, expecting the addition of 230,000 jobs.

Developed economies worldwide continue to struggle with the side effects of the global financial crisis, and while growth in the U.S. is picking up, Fed officials have voiced concern that it still isn't fast enough to ensure healthy employment.

"The picture for all [major] currencies remains challenging," said Thomas Kressin, currencies portfolio manager at Pacific Investment Management Co., which has $2 trillion in assets under management. "We are in a new normal in which rates are going to remain low for a significant period." But Mr. Kressin, who didn't disclose his position, notes that the dollar is less vulnerable than the euro.

"U.S. data point to a stronger economic cycle, and the Fed could start tightening in 2015," he said. "This is out of sight in the euro zone."

While many investors perceive the Fed to be adopting a more hawkish tone, the European Central Bank left the door open to additional stimulus in June, when it cut benchmark interest rates.

Europe emerged from a recession in the second quarter of 2013 but since then economic indicators have been more mixed than in the U.S.

"On the monetary slopes, the U.S. is getting ready for takeoff whilst the ECB is still looking down the slopes from a dizzy height," HSBC currencies strategist David Bloom wrote in a research note on Thursday.

Money managers such as hedge funds as a group hold the most bets on the dollar rising against the euro since November 2012, according to the latest data from the U.S. Commodity Futures Trading Commission.

Insight Investments, which has $470 billion under management, has for several months bet against the euro. But fund managers there put on fresh wagers on the dollar last week.

"Going forward it will be the performance of the dollar rather than the euro that will determine the path for the exchange rate," said Paul Lambert, currency manager at the firm.

Write to Chiara Albanese at chiara.albanese@wsj.com