The mission would have a mandate for a year which could be extended if both sides request it.
Negotiators for the two sides issued a joint request for the UN's involvement last week during peace talks in Cuba.
They have set a deadline of 23 March for the signing of a peace accord.
The UN "political mission" will consist of unarmed observers from Latin American and Caribbean nations.
Colombia has seen decades of fighting between the government and the left-wing Farc movement, with more than 220,000 people killed and millions displaced in unrest which has also involved other guerrilla groups and right-wing paramilitaries.  It is the longest-running armed conflict in the Western Hemisphere.
"It isn't common for a country to refer itself to the council, but it's exactly the kind of role the United Nations should be playing," said British UN Ambassador Matthew Rycroft.
"I hope today will mark the start of the final stage of peace talks."
US Ambassador Samantha Power warned that issues between the two sides still needed to be resolved, such as the removal of land mines and the re-integration of guerrillas into the population.
The UN resolution asks Secretary-General Ban Ki-moon to make detailed recommendations on the  mission's size and operation to be approved by the security council within 30 days of a ceasefire.
Last week, the Colombian government's lead negotiator, Humberto de la Calle, described the request to the UN as a "transcendental" moment.
He said it was an "unequivocal demonstration of our desire to end confrontation".
Since official peace talks started in Havana in November 2012, negotiators have reached agreement on key issues such as the political participation of the rebels, land rights, drug trafficking and transitional justice.
Last September, President Juan Manuel Santos and Farc chief Timoleon Jimenez, known as Timochenko, said they wanted an agreement within six months.

A spokesman said the closure was part of a wider plan of "simplifying the business", which has already seen the closure of about 40 branches in the UK.
He said the branch handled Â£400m from 16,000 customers, with 6,000 in Guernsey and 2,000 to 3,000 in Jersey.
The spokesman said a factor in the decision was the high cost of operating in an offshore banking centre.
The branch is the only one in the Channel Islands.
He said account holders would be contacted directly over the next few days to outline what he described as the "next steps", but customers should not be concerned and mortgages would continue to be honoured.
The company would look to find room for its employees elsewhere in its business, the spokesman added.
The UN Security Council has approved the creation of an unarmed mission in Colombia to oversee a bilateral ceasefire, if Farc rebels and the government sign a peace agreement.
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The Guernsey branch of the Co-operative Bank is to close early next year with the loss of 11 jobs.