China's benchmark Shanghai Composite was up 2.59% to 2,996.58 in afternoon trade.
Hong Kong's benchmark Hang Seng index was up 1.71% to 20,714.23.
Analysts said Ms Yellen's remarks had improved investors' appetite for risk.
"Many investors have been haunted by looming US rate hikes, which is like a sword hanging over the head," equity trading head of Shanshan Finance Wu Kan said.
"Yellen's remarks gave investors some breathing space, and improved risk appetite."
Two Chinese lenders made their debut in Hong Kong on Wednesday - Zheshang Bank and Bank of Tianjin.
Together the banks raised a combined $2.6bn (Â£1.8bn), however their shares were trading lower than their initial offer price as investors continue to be wary of non-performing loans and the earnings potential of some of China's lenders.
Elsewhere, stocks in Australia were higher after touching a near one-month low on Tuesday. Sydney's S&P/ASX 200 closed up 0.12% to 5,010.3 points.
Shares in Virgin Australia lost 9.5% in Sydney trade after the carrier's biggest shareholder, Air New Zealand, said it might sell its 26% stake.
Virgin Australia has been struggling in the domestic market against larger carrier Qantas.
Meanwhile, South Korea's Kospi index also finished the session in positive territory, up 0.36% to 2,002.14.
Japan was the one major index in negative territory on Wednesday following disappointing official industrial output numbers.
The figures showed output falling 6.2% in February from a month earlier, marking the biggest drop since the 2011 tsunami.
Some of Japan's big exporters lost ground on a stronger yen against the dollar, which fell after Ms Yellen's comments.
Toyota finished down 2.5%, while Nissan closed down 3.7%.
Meanwhile, shares in airbag maker Takata fell 19.5% on a news report that the firm's recall costs could amount to as much as $24bn.
The Nikkei 225 finished the session down 1.31% to 16,878.96.
Markets in Asia were largely in positive territory on Wednesday after US Federal Reserve chair Janet Yellen said the Fed should "proceed cautiously" before raising interest rates.