After hours of late-night talks Prime Minister Theresa May was given until the end of October to pass her deal for leaving the bloc through parliament, having failed three times already.
The extension allows for an earlier exit if May achieves it, with a review taking place on June 21.
News of the delay allowed traders to breathe a sigh of relief and the pound edged up against the dollar and euro, though the gains were limited with the agreement merely kicking the can down the road.
And there remains much uncertainty, with the prime minister under intense pressure from hardline Brexit supporters in her Conservative party not to compromise in her talks with the opposition Labour party, and the discussions are moving slowly.
Asian equity markets fell, with few catalysts to drive buying and investors still on edge over a brewing trade battle between the United States and Europe.
White House threats this week to hammer $11 billion worth of EU goods with tariffs jolted markets, which have been rallying this year on optimism that China and the US were close to ending their own battle.
The warning revived concerns about Donald Trump's protectionist agenda that has taken aim at all US trading partners.
In early trade Hong Kong was down 0.6 percent and Shanghai shed 0.4 percent while Tokyo went into the break 0.3 percent lower.
Sydney fell 0.5 percent, Seoul and Taipei were each 0.1 percent lower, while Manila and Jakarta shed 0.4 percent apiece. Singapore added 0.5 percent and Wellington rose 0.6 percent.
Regional investors were also unmoved by the latest central bank dovishness.
The Federal Reserve released minutes of its March meeting that reinforced expectations that it will not lift interest rates this year as it keeps an eye on the US economy and brewing risks abroad.
"I think this confirms the message that we got from the March meeting," James McCann, senior economist at Aberdeen Standard Investments, told Bloomberg News. "This is a Fed that's pretty happy to just sit on its hands for the time being and stay on hold and see how some of these cross currents play out."