After the bill was passed, Canadian Prime Minister Justin Trudeau tweeted, "It's been too easy for our kids to get marijuana, and for criminals to reap the profits".
The bill is likely to receive Royal Assent this week, and the government will then choose an official date when the law will come into force.
It also allows adults to sell cannabis as well as grow up to four plants in their home, making Canada the second country in the world after Uruguay to legalize recreational marijuana use, and the first G7 nation to do so.
Canada criminalized pot possession in 1923, but became an early adopter of medical marijuana in 2001.
The Senate's amendment was meant to head off any legal challenges to the provinces' constitutional authority to prohibit home cultivation.
He has insisted his government would move to legalize the production, sale and consumption of the drug this year. That timeline was pushed back after the Senate requested more time to review Bill C-45.
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When you see innocent kids being put in tents sleeping on floor after getting ripped from their parents and your response is "Did they come here legally?", then we don't have a difference in political opinion.
The government rejected 12 other amendments approved by the Senate.
Based on consumption data from past year, Statistics Canada has estimated that the market will be worth Can$5.7 billion (€3.7 billion).
Canada's Senate has passed the federal government's bill to legalize recreational marijuana on a national level.
Some senators have risen to argue that the upper chamber has done its due diligence and now is the time to concede to the will of the elected House of Commons, and pass the legislation.
As for cannabis tax haul, Finance Minister Bill Morneau has estimated a total of $400 million (€260 million), although Ottawa has agreed to retain only 25 per cent of the total raised and put the rest into provincial government coffers.
He said the federal government received valuable advice from Colorado and other US states that have legalized recreational marijuana.