The upbeat outlook for the crises provided a catalyst for an equities rally in Europe and the United States, a mantle picked up in bourses across Asia.
Asian markets mostly rose Friday after European leaders and Russia agreed a plan to end Ukraine's 10-month war, while traders were confident Greece would eventually hammer out a debt overhaul with its creditors.
Hong Kong rose 0.46 percent, Shanghai added 0.50 percent and Seoul put on 0.33 percent, while Sydney rallied 1.09 percent as energy firms were boosted by a rebound in oil prices.
But Tokyo, which hit a seven-year high Thursday, slipped 0.31 percent.
After 17-hour talks the leaders of Ukraine, Russia, France and Germany on Thursday hammered out a blueprint to end the conflict between Kiev and pro-Moscow rebels.
The ceasefire is to take effect at midnight Sunday (2200 GMT on Saturday) in Ukraine and heavy weapons are to be withdrawn from frontlines.
However, while the deal was welcomed on all sides, leaders remain cautious, with German Chancellor Angela Merkel saying "I have no illusions. We have no illusions", adding that "much work" remained.
The news pushed European stocks higher, with Frankfurt up 1.56 percent, Paris adding 1.00 percent and London 0.15 percent higher.
And on Wall Street the Dow added 0.62 percent, the S&P 500 jumped 0.96 percent -- both close to record highs -- and the Nasdaq surged 1.18 percent to levels not seen since 2000.
'Glass half full'
“People are looking at the glass half full,” John Carey, a Boston-based fund manager at Pioneer Investment Management, told Bloomberg News.
“There’s general optimism around the US economy and a little bit of relief that some of the major international issues are not going to impinge just yet on positive trends here.”
Hopes for a breakthrough in the Greek crisis also provided support as the country's new Prime Minister Alexis Tsipras presented his case for an overhaul of its bailout programme to EU leaders including Merkel, the strongest opponent of his plans.
Tsipras said Athens would start technical talks with eurozone partners on Friday in a bid to find common ground before a last-ditch meeting of finance ministers on Monday.
Global markets are hoping a deal can be reached before the end of the month, when Greece's bailout is due to expire. Failure to agree an extension would see it default on its giant debts and likely mean it would crash out of the eurozone.
The European Central Bank also provided a lift when it increased the volume of emergency cash available to Greek banks, easing concerns over liquidity that had led to speculation of a possible run on the country's lenders.
The euro bought $1.1400 and 135.60 yen, compared with $1.1406 and 135.70 yen in New York.
The dollar was at 119.01 yen early Friday, compared with 118.97 yen in US trade.
On oil markets, prices fell after steep gains in the previous session that were fuelled by planned investment cuts by the world's leading petroleum producers.
US benchmark West Texas Intermediate for March delivery fell seven cents to $51.14 while Brent crude for April was down eight cents to $59.20.
Gold fetched $1,223.45 an ounce, against $1,223.20 on Thursday.