The resolution was proposed by France, which sent forces to northern Mali in January to drive out Islamist militants who took advantage of a March 2012 coup of the Malian government.
France began withdrawing some of its 4,000 troops in Mali earlier this month, but will retain 1,000 in the country, the BBC said.
U.N. peacekeepers could be in Mali by midsummer, taking over duties from a 6,000-member African-led force terms of the U.N. resolution indicate.
The resolution calls for a one-year mission with up to 11,200 military personnel and 1,400 police who would assume their duties July 1 and will include some of the African-led force.
Mali devolved into chaos last year in a military coup, which allowed ethnic Tuaregs and later al-Qaida-linked militants to seize the northern portion of the former French colony. French and African troops have helped drive the militants from major towns but attacks still occur.
The U.N. force will stretch the definition of peacekeeper, since there is no peace agreement to enforce in Mali, the BBC commented.