In Tokyo, the common currency rose to $1.1241, from $1.1234 in New York.
The euro had briefly tumbled to $1.1098 - its lowest level since September 2003 - in Asia on Monday, owing to fears the poll result could lead to a Greek exit from the eurozone.
The single currency eased to 132.85 yen from 133.12 yen in US trade, although it is still up from levels below 132 yen on Monday in Japan.
Victory for the far-left Syriza in Sunday's poll initially sparked fears Athens will refuse to stick to its bailout obligations and eventually leave the eurozone. The party had campaigned on renegotiating terms of the lifeline, which include major spending cuts and painful tax hikes.
But "they don't seem to have what I'd view as a far-left goal -- it's not like they're going to come out and default on all their debt," Matt Derr, a foreign-exchange strategist at Credit Suisse Group AG, told Bloomberg News.
"The euro is getting a bit of a relief rally."
A scourge of austerity policies who calls himself an "accidental economist" is set to become Greece's finance minister and the key negotiator with its creditors, barring last-minute hitches, senior Syriza party officials said on Monday.
In characteristically purple prose, Yanis Varoufakis, 53, celebrated the victory of Alexis Tsipras's far-left Syriza in Greek elections by paraphrasing Welsh poet Dylan Thomas.
"Greek democracy today chose to stop going gently into the night. Greek democracy resolved to rage against the dying of the light," the bi-national Greek-Australian wrote on his blog.
The dollar was mixed against other Asia-Pacific currencies.
It strengthened to 44.15 Philippine pesos from 44.11 pesos on Monday, and to 61.45 Indian rupees from 61.43 rupees.
The greenback weakened to Tw$31.27 from Tw$31.29, to 12,465 Indonesian rupiah from 12,510 rupiah, to Sg$1.3441 from Sg$1.3454, and to 32.57 Thai baht from 32.58 baht.
It was also at 1,079.75 South Korean won against 1,079.53 won.
The Australian dollar - which fell below 80 cents last week for the first time since mid-2009 as metal prices fell - rose to 79.38 US cents from 78.80 cents.
The Chinese yuan rose to 18.90 yen from 18.82 yen.