By Tommy Stubbington 

European stocks closed strongly higher on Wednesday after Greece's prime minister said its country is close to reaching a deal with its creditors.

However, European Commission Vice President Valdis Dombrovskis played down the idea of a quick agreement, saying Greece and its creditors still have a way to go before a deal is reached.

The Stoxx Europe 600 ended 1.3% higher, recovering the losses it suffered on Tuesday. Germany's DAX closed up 1.3%, the U.K.'s FTSE 100 rose 1.2%, and France's CAC 40 climbed 2%.

There were also gains on Wall Street, with the Dow Jones Industrial Average trading 0.6% higher at the European close, recovering from Tuesday's 1% slump .

Greek officials have been holding negotiations with eurozone and International Monetary Fund officials in Brussels for weeks, and on Wednesday Greek Prime Minister Alexis Tsipras said the country is close to an agreement with its international creditors over its rescue program.

Investors took this news positively. The Greek stock market closed 3.6% higher, with the country's banking stocks posting strong gains.

Adding to the positive tone for investors was a degree of clarity in a few major corporate deals.

Alcatel-Lucent SA was one of the biggest gainers, closing almost 5% higher after executives on Tuesday defended their plan to sell their company to Finland's Nokia Corp., telling shareholders that it was the only option for a company that lacks "critical mass" against giants such as Ericsson and Huawei Technologies.

Shares in Imperial Tobacco Group PLC also rose sharply after U.S. antitrust enforcers on Tuesday cleared Reynolds American to proceed with its $25 billion acquisition of Lorillard Inc., ending months of uncertainty about the U.S. cigarette makers' plan to combine.

The euro steadied after the previous session's losses, when it had fallen around 1% on the day to a fresh one-month low. The common currency was 0.2% higher against the dollar at $1.0896 late in the afternoon Wednesday.

Greek government bonds recovered slightly, with the two-year yield down more than 1.7 percentage points at 22.8%. Yields fall as prices rise. Still, yields remain at levels that indicate investors are acutely worried about a default.

In commodities markets, Brent crude fell 0.9% to $63.18 a barrel, and gold was broadly steady at $1,187 an ounce.

Josie Cox contributed to this article.

Write to Tommy Stubbington at tommy.stubbington@wsj.com