Japan's Nikkei shot up 3.1 percent, helped in part by a pullback in the yen, while South Korea added 1.5 percent.
The dollar fell for a third consecutive day against its rivals on Monday on growing bets the US central bank will press the pause button on its rate hike cycle in the coming months.
"Market sentiment has improved", said Gao Qi, a strategist at Scotiabank. "I do think going forward you are probably not likely to see that type of move where equities sell off 20 percent in the space of six weeks, but generally volatility will be higher than what you saw in 2017 and the first half of 2018".
Stocks across Asia kicked off the week with strong gains after soothing Federal Reserve comments and an easing of monetary policy in China stoked a renewed appetite for risk assets.
Despite Friday's stronger than expected U.S. Decemberjobs data, many analysts believe the world's largest economy is losing momentum and further rate hikes are the last thing it needs. Bostic, who is not a voting member of the Federal Open market Committee this year, said the Fed may only need to raise rates once in 2019.
The Federal Reserve may only need to raise interest rates once in 2019, Atlanta Fed President Raphael Bostic said on Monday, focusing on business executives' nervousness about the economy and a global slowdown as factors that may hold the USA central bank back.
The US dollar had gained 4.3 per cent in 2018 as the Fed hiked rates four times on the back of a strong domestic economy, falling unemployment and rising wage pressures.
"Last Friday's strong USA jobs data suggested that recession fears were overblown", said Philip Wee, currency strategist at DBS in a note.
Wee said he still expects the Fed to hike rates twice this year. The Bloomberg Dollar Spot Index dipped 0.2 percent.The euro bought $1.1415, up 0.2 percent.The pound rose 0.2 percent to $1.2749. The move frees up $116 billion for new lending as it tries to reduce the risk of a pronounced fall in the pace of economic growth.
US officials are meeting their counterparts in Beijing this week for the first face-to-face talks since US President Donald Trump and Chinese President Xi Jinping agreed in December to a 90-day truce in a trade war that has roiled global markets.
The People's Bank of China said on Friday it would cut the amount of cash lenders must hold as reserves.
The dollar lost 0.2 percent versus the offshore yuan to 6.8490.
The two sides have until March 1 to make a deal, after which Trump has pledged to ramp up tariffs to 25 percent, from 10 percent, on $200 billion worth of Chinese imports.
Brent crude futures rose 27 cents to settle at $57.33 a barrel, a 0.47 percent gain.
Elsewhere, the Australian dollar was lower by 0.07 per cent at US$0.7141.