Toronto's S&P/TSX composite index closed up 122.15 points at 14,533.22, building on another triple-digit gain Friday when news of a likely agreement on Greek debt began to emerge.
In New York, the Dow Jones industrial average shot up 217.27 points to 17,977.68 after soaring almost 212 points on Friday.
The Nasdaq also enjoyed another big day, rising 73.81 points to 5,071.51 on top of a 75-point gain the previous session, while the S&P 500 advanced 22.98 points to 2,099.60.
The strength on North American markets followed a rally on European bourses that saw Germany's DAX climb 1.4 per cent, while France's CAC 40 surged two per cent and Britain's FTSE 100 rose 0.7 per cent.
On the New York Mercantile Exchange, the August crude contract was down 54 cents at US$52.20 a barrel, while August gold fell $2.50 to US$1,155.40 an ounce.
Meanwhile, the loonie continued to trend lower, down 0.38 of a U.S. cent at 78.49 cents amid speculation that the Bank of Canada may cut its trend-setting policy rate on Wednesday.
The tentative deal on Greece's debt woes was announced early Monday, some nine hours after a self-imposed deadline by negotiators had passed.
The three-year loan program providing about 85 billion euros in bailout loans would remove the immediate threat of Athens defaulting on its debts, shore up its banks and prevent the country from leaving the euro. Creditors have also indicated that a future debt restructuring might be possible.
However, Prime Minister Alexis Tsipras still has to get tough austerity measures that include tax increases and pension and labour market reforms through the Greek parliament in the face of strong opposition even within his own Syriza party.
A group of party traditionalists, known as the Left Platform, denounced the agreement as the "worst deal possible ... that maintains the country's status: a debt colony under a German-run European Union."
And the government's junior coalition partner immediately said it cannot back the agreement, describing it as a German-led "coup."
Craig Fehr, Canadian markets strategist at Edward Jones in St. Louis, agreed there are definite risks ahead.
"I wouldn't advise anybody to get too euphoric over the prospects of a deal, which is what I think we have to call it at this point, the prospects of a deal," he said.
Nevertheless, Fehr contrasted that with the mood last week when "it was apparent that, at least on certain days, the kind of the worst-case scenario (of an economic collapse by Greece and its exit from the euro) was being baked into the market."
"So I think we're seeing a little bit of a rally on the fact that at least that most adverse outcome appears to be off the table, at least for the moment."