|Logo of the London Stock Exchange. (AFP PHOTO/FILES/CARL DE SOUZA)|
The Fed chair "left the door cracked open for a softer stance on rate hikes (or the lack thereof)," said Briefing.com analyst Patrick O'Hare.
Yellen, in prepared testimony ahead of a congressional hearing, said that she would "carefully monitor" US economic conditions as the labour market tightens but that inflation was lagging behind the Fed's targets.
Further comments during Yellen's two-day congressional testimony will be pored over for further clues about future monetary policy.
"Equities are nicely positive at half-time with all three of our indices in the midst of potentially attractive bullish breakouts that could open the door for a return to recent record highs," said Mike van Dulken, an analyst at Accendo Markets.
"Wednesday promises to be quite an entertaining day for markets, with central banks once again the focus as the Bank of Canada announces its latest monetary policy decision and Federal Reserve Chair Janet Yellen begins her two-day testimony," said Oanda analyst Craig Erlam.
"Yellen will likely be quizzed on a number of issues related to the Fed's plans, including its plans for interest rates beyond the end of the year," he said.
"Yellen likes to keep her cards very close to her chest though so may give little new information away today, not that this often stops markets getting carried away," he added.
Oil prices, which have seen wild swings in recent months, bounced back from losses last week with gains of more than one percent Tuesday on bets that US stockpiles had fallen.
Comments from the OPEC cartel that its output cuts with Russia were bearing fruit were also welcomed.
But investors remained wary as the turmoil surrounding US President Donald Trump intensified on Tuesday when his son Donald Jr released emails showing he had embraced Russia's efforts to support the tycoon's presidential campaign against Hillary Clinton.
The news is the latest blow to the White House, which has been battered by accusations over Russian collusion and cover-ups - fuelling worries about the president's ability to push through his business- and market-friendly economic agenda.
Key figures around 1545 GMT:
New York - DOW: UP 0.6 per cent at 21,529.73 points
London - FTSE 100: UP 1.2 per cent at 7,416.93 (close)
Frankfurt - DAX 30: UP 1.5 per cent at 12,626.58 (close)
Paris - CAC 40: UP 1.6 per cent at 5,222.13 (close)
Tokyo - Nikkei 225: DOWN 0.5 per cent at 20,098.38 (close)
Hong Kong - Hang Seng: UP 0.6 per cent at 26,043.64 (close)
Shanghai - Composite: DOWN 0.2 per cent at 3,197.54 (close)
Euro/dollar: FLAT at US$1.1413
Pound/dollar: UP at US$1.2889 from US$1.2867
Dollar/yen: FLAT at 113.20 yen
Oil - Brent North Sea: UP 19 cents at US$47.71 per barrel
Oil - West Texas Intermediate: UP 38 cents at US$45.42