The Fed held interest rates steady as expected on Wednesday but discarded pledges of "further gradual increases" in interest rates, and said it would be "patient" before making any further moves amid a cloudy outlook for the US economy due to global headwinds.
The dollar index, a gauge of its value versus six major peers, had been trading lower ahead of the meeting and for much of the week. Following the Fed meeting, it fell to a three-week low of 95.246.
Analysts have turned bearish on the dollar, which outperformed last year thanks to rates expectations and a robust US economy, however the trade war and pressure on global growth have threatened to dent domestic output.
The Indonesian rupiah, which was one of the worst performers in 2018, jumped 1.2 percent against the dollar to 13,960, its strongest level since the end of June last year. It fell 6 percent in 2018 but is set to end January nearly 3 percent higher.
The strong gains were followed by the South Korean won and Thai baht, which rose 0.6 percent and 0.4 percent, respectively, against the dollar.
Meanwhile, Malaysia's ringgit rose 0.5 percent to its strongest level in nearly six months after exports in December grew better-than-expected.
With the Fed meeting out of the way, investors will now turn their focus to the outcome of the US-China trade talks, which could cap some of the more upbeat sentiment seen on Thursday with little indication Beijing is willing to address core US demands.
"We don't expect any earth shattering announcements in terms of an immediate resolution of all pending issues but at the very minimum there should be a statement affirming the progress made in negotiations," said Wei Liang Chang, a FX strategist at Mizuho Bank.
Maybank analysts said in a note a lack of any material progress in talks could disrupt the risk-seeking play investors are undertaking on Thursday.
The Indian rupee rose 0.1 percent to 71.04. The government will announce its final budget ahead of a looming general election on Friday, with the uncertain outcome proving a concern for investors.